In this paper, we establish the existence of the global weak solutions for the non-homogeneous incompressible magnetohydrodynamic equations with Navier boundary condi-tions for the velocity field and the magnetic fiel...In this paper, we establish the existence of the global weak solutions for the non-homogeneous incompressible magnetohydrodynamic equations with Navier boundary condi-tions for the velocity field and the magnetic field in a bounded domain Ω R^3. Furthermore,we prove that as the viscosity and resistivity coefficients go to zero simultaneously, these weaksolutions converge to the strong one of the ideal nonhomogeneous incompressible magneto-hydrodynamic equations in energy space.展开更多
We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectl...We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain Ω⊂R^(3).It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic equations in a finite time interval which is independent of the viscosity coefficient and the magnetic diffusivity coefficient.The solution is uniformly bounded in a conormal Sobolev space and W^(1,∞)(Ω)which allows us to take the zero kinematic viscosity-magnetic diffusion limit.Moreover,we also get the rates of convergence in L^(∞)(0,T;L^(2)),L^(∞)(0,T;W^(1,p))(2≤p<∞),and L^(∞)((0,T)×Ω)for some T>0.展开更多
This paper deals with superlinear fourth-order elliptic problem under Navier boundary condition. By using the mountain pass theorem and suitable truncation, a multiplicity result is established for all λ〉 0 and some...This paper deals with superlinear fourth-order elliptic problem under Navier boundary condition. By using the mountain pass theorem and suitable truncation, a multiplicity result is established for all λ〉 0 and some previous result is extended.展开更多
In this paper a semilinear biharmonic problem involving nearly critical growth with Navier boundary condition is considered on an any bounded smooth domain. It is proved that positive solutions concentrate on a point ...In this paper a semilinear biharmonic problem involving nearly critical growth with Navier boundary condition is considered on an any bounded smooth domain. It is proved that positive solutions concentrate on a point in the domain, which is also a critical point of the Robin’s function corresponding to the Green’s function of biharmonic operator with the same boundary condition. Similar conclusion has been obtained in [6] under the condition that the domain is strictly convex.展开更多
We study positive solutions of the following polyharmonic equation with Hardy weights associated to Navier boundary conditions on a half space:where rn is any positive integer satisfying 0 〈 2m 〈 n. We first prove ...We study positive solutions of the following polyharmonic equation with Hardy weights associated to Navier boundary conditions on a half space:where rn is any positive integer satisfying 0 〈 2m 〈 n. We first prove that the positive solutions of (0.1) are super polyharmonic, i.e.,where x* = (x1,... ,Xn-1, --Xn) is the reflection of the point x about the plane Rn-1. Then, we use the method of moving planes in integral forms to derive rotational symmetry and monotonicity for the positive solution of (0.3), in which α can be any real number between 0 and n. By some Pohozaev type identities in integral forms, we prove a Liouville type theorem--the non-existence of positive solutions for (0.1).展开更多
In this paper, we consider a p(x)-biharmonic problem with Navier boundary conditions. The existence of infinitely many solutions which tend to zero is investigated based on the symmetric Mountain Pass lemma. Our app...In this paper, we consider a p(x)-biharmonic problem with Navier boundary conditions. The existence of infinitely many solutions which tend to zero is investigated based on the symmetric Mountain Pass lemma. Our approach relies on the theory of variable exponent Sobolev space.展开更多
In this paper,we focus on the immiscible compressible two-phase flow described by the coupled compressible Navier-Stokes system and the modified Allen-Cahn equations.The generalized Navier boundary condition and the r...In this paper,we focus on the immiscible compressible two-phase flow described by the coupled compressible Navier-Stokes system and the modified Allen-Cahn equations.The generalized Navier boundary condition and the relaxation boundary condition are established in order to solve the problem of moving contact lines on the solid boundary by using the principle of minimum energy dissipation.The existence and uniqueness for local strong solution in three dimensional bounded domain for this type of boundary value problem is obtained by the elementary energy method and the maximum principle.展开更多
We propose an efficient numerical method for the simulation of the twophase flows with moving contact lines in three dimensions.The mathematical model consists of the incompressible Navier-Stokes equations for the two...We propose an efficient numerical method for the simulation of the twophase flows with moving contact lines in three dimensions.The mathematical model consists of the incompressible Navier-Stokes equations for the two immiscible fluids with the standard interface conditions,the Navier slip condition along the solid wall,and a contact angle condition(Ren et al.(2010)[28]).In the numerical method,the governing equations for the fluid dynamics are coupledwith an advection equation for a level-set function.The latter models the dynamics of the fluid interface.Following the standard practice,the interface conditions are taken into account by introducing a singular force on the interface in themomentum equation.This results in a single set of governing equations in the whole fluid domain.Similarly,the contact angle condition is imposed by introducing a singular force,which acts in the normal direction of the contact line,into theNavier slip condition.The newboundary condition,which unifies the Navier slip condition and the contact angle condition,is imposed along the solid wall.The model is solved using the finite difference method.Numerical results are presented for the spreading of a droplet on both homogeneous and inhomogeneous solid walls,as well as the dynamics of a droplet on an inclined plate under gravity.展开更多
The effects of the Born repulsive force on the stability and dynamics of ultra-thin slipping films under the influences of intermolecular forces are investigated with bifurcation theory and numerical simulation. Resul...The effects of the Born repulsive force on the stability and dynamics of ultra-thin slipping films under the influences of intermolecular forces are investigated with bifurcation theory and numerical simulation. Results show that the repulsive force has a stabilizing effect on the development of perturbations, and can suppress the rupture process induced by the van der Waals attractive force. Although slippage will enhance the growth of disturbances, it does not have influence on the linear cutoff wave number and the final shape of the film thickness as time approaches to infinity.展开更多
In this paper,we compute a phase field(diffuse interface)model of CahnHilliard type for moving contact line problems governing the motion of isothermal multiphase incompressible fluids.The generalized Navier boundary ...In this paper,we compute a phase field(diffuse interface)model of CahnHilliard type for moving contact line problems governing the motion of isothermal multiphase incompressible fluids.The generalized Navier boundary condition proposed by Qian et al.[1]is adopted here.We discretize model equations using a continuous finite element method in space and a modified midpoint scheme in time.We apply a penalty formulation to the continuity equation which may increase the stability in the pressure variable.Two kinds of immiscible fluids in a pipe and droplet displacement with a moving contact line under the effect of pressure driven shear flow are studied using a relatively coarse grid.We also derive the discrete energy law for the droplet displacement case,which is slightly different due to the boundary conditions.The accuracy and stability of the scheme are validated by examples,results and estimate order.展开更多
文摘In this paper, we establish the existence of the global weak solutions for the non-homogeneous incompressible magnetohydrodynamic equations with Navier boundary condi-tions for the velocity field and the magnetic field in a bounded domain Ω R^3. Furthermore,we prove that as the viscosity and resistivity coefficients go to zero simultaneously, these weaksolutions converge to the strong one of the ideal nonhomogeneous incompressible magneto-hydrodynamic equations in energy space.
基金supported partially by NSFC(11671193,11971234)supported partially by the China Postdoctoral Science Foundation(2019M650581).
文摘We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain Ω⊂R^(3).It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic equations in a finite time interval which is independent of the viscosity coefficient and the magnetic diffusivity coefficient.The solution is uniformly bounded in a conormal Sobolev space and W^(1,∞)(Ω)which allows us to take the zero kinematic viscosity-magnetic diffusion limit.Moreover,we also get the rates of convergence in L^(∞)(0,T;L^(2)),L^(∞)(0,T;W^(1,p))(2≤p<∞),and L^(∞)((0,T)×Ω)for some T>0.
基金The 985 Program of Jilin Universitythe Science Research Foundation for Excellent Young Teachers of College of Mathematics at Jilin University
文摘This paper deals with superlinear fourth-order elliptic problem under Navier boundary condition. By using the mountain pass theorem and suitable truncation, a multiplicity result is established for all λ〉 0 and some previous result is extended.
基金The research work was supported by the National Natural Foundation of China (10371045)Guangdong Provincial Natural Science Foundation of China (000671).
文摘In this paper a semilinear biharmonic problem involving nearly critical growth with Navier boundary condition is considered on an any bounded smooth domain. It is proved that positive solutions concentrate on a point in the domain, which is also a critical point of the Robin’s function corresponding to the Green’s function of biharmonic operator with the same boundary condition. Similar conclusion has been obtained in [6] under the condition that the domain is strictly convex.
文摘We study positive solutions of the following polyharmonic equation with Hardy weights associated to Navier boundary conditions on a half space:where rn is any positive integer satisfying 0 〈 2m 〈 n. We first prove that the positive solutions of (0.1) are super polyharmonic, i.e.,where x* = (x1,... ,Xn-1, --Xn) is the reflection of the point x about the plane Rn-1. Then, we use the method of moving planes in integral forms to derive rotational symmetry and monotonicity for the positive solution of (0.3), in which α can be any real number between 0 and n. By some Pohozaev type identities in integral forms, we prove a Liouville type theorem--the non-existence of positive solutions for (0.1).
基金supported in part by the NNSF of China(Grant No.11101145)Research Initiation Project for Highlevel Talents(201031)of North China University of Water Resources and Electric Power
文摘In this paper, we consider a p(x)-biharmonic problem with Navier boundary conditions. The existence of infinitely many solutions which tend to zero is investigated based on the symmetric Mountain Pass lemma. Our approach relies on the theory of variable exponent Sobolev space.
基金supported by the National Natural Science Foundation of China(Nos.12171024,11901025,11971217,11971020)。
文摘In this paper,we focus on the immiscible compressible two-phase flow described by the coupled compressible Navier-Stokes system and the modified Allen-Cahn equations.The generalized Navier boundary condition and the relaxation boundary condition are established in order to solve the problem of moving contact lines on the solid boundary by using the principle of minimum energy dissipation.The existence and uniqueness for local strong solution in three dimensional bounded domain for this type of boundary value problem is obtained by the elementary energy method and the maximum principle.
基金partially supported by Singapore MOE AcRF grants(R-146-000-285-114,R-146-000-327-112)NSFC(NO.11871365)supported by the National Natural Science Foundation of China(NO.12071190).
文摘We propose an efficient numerical method for the simulation of the twophase flows with moving contact lines in three dimensions.The mathematical model consists of the incompressible Navier-Stokes equations for the two immiscible fluids with the standard interface conditions,the Navier slip condition along the solid wall,and a contact angle condition(Ren et al.(2010)[28]).In the numerical method,the governing equations for the fluid dynamics are coupledwith an advection equation for a level-set function.The latter models the dynamics of the fluid interface.Following the standard practice,the interface conditions are taken into account by introducing a singular force on the interface in themomentum equation.This results in a single set of governing equations in the whole fluid domain.Similarly,the contact angle condition is imposed by introducing a singular force,which acts in the normal direction of the contact line,into theNavier slip condition.The newboundary condition,which unifies the Navier slip condition and the contact angle condition,is imposed along the solid wall.The model is solved using the finite difference method.Numerical results are presented for the spreading of a droplet on both homogeneous and inhomogeneous solid walls,as well as the dynamics of a droplet on an inclined plate under gravity.
基金Project supported by the National Natural Science Foundation of China (Grant No:10472062 ) and Shanghai Leading Academic Discipline Project (Grant No: Y0103 ).
文摘The effects of the Born repulsive force on the stability and dynamics of ultra-thin slipping films under the influences of intermolecular forces are investigated with bifurcation theory and numerical simulation. Results show that the repulsive force has a stabilizing effect on the development of perturbations, and can suppress the rupture process induced by the van der Waals attractive force. Although slippage will enhance the growth of disturbances, it does not have influence on the linear cutoff wave number and the final shape of the film thickness as time approaches to infinity.
基金Zhenlin Guo is partially supported by the 150th Anniversary Postdoctoral Mobility Grants(2014-15 awards)and the reference number is PMG14-1509Shuangling Dong is supported by the National Natural Science Foundation of China(No.51406098)And also thank the China Postdoctoral Science Foundation(No.2014M560967).
文摘In this paper,we compute a phase field(diffuse interface)model of CahnHilliard type for moving contact line problems governing the motion of isothermal multiphase incompressible fluids.The generalized Navier boundary condition proposed by Qian et al.[1]is adopted here.We discretize model equations using a continuous finite element method in space and a modified midpoint scheme in time.We apply a penalty formulation to the continuity equation which may increase the stability in the pressure variable.Two kinds of immiscible fluids in a pipe and droplet displacement with a moving contact line under the effect of pressure driven shear flow are studied using a relatively coarse grid.We also derive the discrete energy law for the droplet displacement case,which is slightly different due to the boundary conditions.The accuracy and stability of the scheme are validated by examples,results and estimate order.