This paper is concerned with the free boundary value problem for multidimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local ...This paper is concerned with the free boundary value problem for multidimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local （in time） existence of a weak solution is established; in particular, the density is positive and the solution is regular away from the free boundary.展开更多
In this paper, we investigate the free boundary value problem （FBVP） for the cylindrically symmetric isentropic compressible Navier-Stokes equations （CNS） with density- dependent viscosity coefficients in the case...In this paper, we investigate the free boundary value problem （FBVP） for the cylindrically symmetric isentropic compressible Navier-Stokes equations （CNS） with density- dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a constant exterior pressure. Under certain assumptions imposed on the initial data, we prove that there exists a unique global strong solution which tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.展开更多
The transport behavior of free boundary value problems for a class ofgeneralized diffusion equations was studied. Suitable similarity transformations were used toconvert the problems into a class of singular nonlinear...The transport behavior of free boundary value problems for a class ofgeneralized diffusion equations was studied. Suitable similarity transformations were used toconvert the problems into a class of singular nonlinear two-point boundary value problems andsimilarity solutions were numerical presented for different representations of heat conductionfunction, convection function, heat flux function, and power law parameters by utilizing theshooting technique. The results revealed the flux transfer mechanism and the character as well asthe effects of parameters on the solutions.展开更多
In this paper by means of generalized shooting method and homotopy technique a numerical method was given for computing free multipoint boundary value problem proposed in the intervention of exchange rate by Cadenilla...In this paper by means of generalized shooting method and homotopy technique a numerical method was given for computing free multipoint boundary value problem proposed in the intervention of exchange rate by Cadenillas and Femaado Zapatero. A numerical example was given for illustrating the validity of this method.展开更多
In the present paper, the primitive equations, which can be used to simulate the large-scale motion of the ocean and atmosphere, are considered in the three-dimensional domain bounded below by a fixed solid boundary a...In the present paper, the primitive equations, which can be used to simulate the large-scale motion of the ocean and atmosphere, are considered in the three-dimensional domain bounded below by a fixed solid boundary and above by a free-moving boundary. The global existence and uniqueness of strong solutions are established, and the long-time convergence to the equilibrium state is shown to be either at an exponential rate for the horizontal periodic domain or at an algebraic rate for the horizontal whole space.展开更多
The free boundary value problems for elliptic differential-operator equations are studied.Several conditions for the uniform maximal regularity with respect to boundary parameters and the Fredholmness in abstract L p-...The free boundary value problems for elliptic differential-operator equations are studied.Several conditions for the uniform maximal regularity with respect to boundary parameters and the Fredholmness in abstract L p-spaces are given.In application,the nonlocal free boundary problems for finite or infinite systems of elliptic and anisotropic type equations are studied.展开更多
In this paper, we mainly study the nonlinear wave configuration caused by shock wave reflection for the TSD （Transonic Small Disturbance） equation and specify the existence and nonexistence of various nonlinear wave...In this paper, we mainly study the nonlinear wave configuration caused by shock wave reflection for the TSD （Transonic Small Disturbance） equation and specify the existence and nonexistence of various nonlinear wave configurations. We give a condition under which the solution of the RR （Regular reflection） for the TSD equation exists. We also prove that there exists no wave configuration of shock wave reflection for the TSD equation which consists of three or four shock waves. In phase space, we prove that the TSD equation has an IR （Irregular reflection） configuration containing a centered simple wave. Furthermore, we also prove the stability of RR configuration and the wave configuration containing a centered simple wave by solving a free boundary value problem of the TSD equation.展开更多
基金partially supported by the NSFC(10871134)the AHRDIHL Project of Beijing Municipality (PHR201006107)
文摘This paper is concerned with the free boundary value problem for multidimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local （in time） existence of a weak solution is established; in particular, the density is positive and the solution is regular away from the free boundary.
基金supported by NNSFC(11101145),supported by NNSFC(11326140 and11501323)China Postdoctoral Science Foundation(2012M520360)+1 种基金Doctoral Foundation of North China University of Water Sources and Electric Power(201032),Innovation Scientists and Technicians Troop Construction Projects of Henan Provincethe Doctoral Starting up Foundation of Quzhou University(BSYJ201314 and XNZQN201313)
文摘In this paper, we investigate the free boundary value problem （FBVP） for the cylindrically symmetric isentropic compressible Navier-Stokes equations （CNS） with density- dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a constant exterior pressure. Under certain assumptions imposed on the initial data, we prove that there exists a unique global strong solution which tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.
基金This work was financially supported by the Cross-Century Talents Projects of Educational Ministry of China and the 973 Key Item (No. G1998061510).]
文摘The transport behavior of free boundary value problems for a class ofgeneralized diffusion equations was studied. Suitable similarity transformations were used toconvert the problems into a class of singular nonlinear two-point boundary value problems andsimilarity solutions were numerical presented for different representations of heat conductionfunction, convection function, heat flux function, and power law parameters by utilizing theshooting technique. The results revealed the flux transfer mechanism and the character as well asthe effects of parameters on the solutions.
文摘In this paper by means of generalized shooting method and homotopy technique a numerical method was given for computing free multipoint boundary value problem proposed in the intervention of exchange rate by Cadenillas and Femaado Zapatero. A numerical example was given for illustrating the validity of this method.
基金supported by National Natural Science Foundation of China (Grant Nos. 11931010, 12226326, and 12226327)supported by National Natural Science Foundation of China (Grant No. 11701053)+2 种基金the Key Research Project of Academy for Multidisciplinary Studies, Capital Normal Universitythe Capacity Building for Sci-Tech Innovation—Fundamental Scientific Research Funds (Grant No. 007/20530290068)the Fundamental Research Funds for the Central Universities (Grant Nos. 0903005203477, 2020CDJQY-A040, and 2020CDJQY-Z001)。
文摘In the present paper, the primitive equations, which can be used to simulate the large-scale motion of the ocean and atmosphere, are considered in the three-dimensional domain bounded below by a fixed solid boundary and above by a free-moving boundary. The global existence and uniqueness of strong solutions are established, and the long-time convergence to the equilibrium state is shown to be either at an exponential rate for the horizontal periodic domain or at an algebraic rate for the horizontal whole space.
文摘The free boundary value problems for elliptic differential-operator equations are studied.Several conditions for the uniform maximal regularity with respect to boundary parameters and the Fredholmness in abstract L p-spaces are given.In application,the nonlocal free boundary problems for finite or infinite systems of elliptic and anisotropic type equations are studied.
基金Supported by the Fundamental Research Funds for Shanghai Dianji University(Grant No.11C417)
文摘In this paper, we mainly study the nonlinear wave configuration caused by shock wave reflection for the TSD （Transonic Small Disturbance） equation and specify the existence and nonexistence of various nonlinear wave configurations. We give a condition under which the solution of the RR （Regular reflection） for the TSD equation exists. We also prove that there exists no wave configuration of shock wave reflection for the TSD equation which consists of three or four shock waves. In phase space, we prove that the TSD equation has an IR （Irregular reflection） configuration containing a centered simple wave. Furthermore, we also prove the stability of RR configuration and the wave configuration containing a centered simple wave by solving a free boundary value problem of the TSD equation.
