This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit,...This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.展开更多
This paper is devoted to studying the zero dissipation limit problem for the one-dimensional compressible Navier-Stokes equations with selected density-dependent viscosity.In particular,we focus our attention on the v...This paper is devoted to studying the zero dissipation limit problem for the one-dimensional compressible Navier-Stokes equations with selected density-dependent viscosity.In particular,we focus our attention on the viscosity taking the formμ(ρ)=ρ^(ϵ)(ϵ>0).For the selected density-dependent viscosity,it is proved that the solutions of the one-dimensional compressible Navier-Stokes equations with centered rarefaction wave initial data exist for all time,and converge to the centered rarefaction waves as the viscosity vanishes,uniformly away from the initial discontinuities.New and subtle analysis is developed to overcome difficulties due to the selected density-dependent viscosity to derive energy estimates,in addition to the scaling argument and elementary energy analysis.Moreover,our results extend the studies in[Xin Z P.Comm Pure Appl Math,1993,46(5):621-665].展开更多
In this paper we have obtained the existence of weak solutions of the small disturbance equations of steady two-dimension flow [GRAPHICS] with Riemann date [GRAPHICS] where v+ greater-than-or-equal-to 0, v- greater-th...In this paper we have obtained the existence of weak solutions of the small disturbance equations of steady two-dimension flow [GRAPHICS] with Riemann date [GRAPHICS] where v+ greater-than-or-equal-to 0, v- greater-than-or-equal-to 0 and u- less-than-or-equal-to u+ by introducing 'artificial' viscosity terms and employing Helley's theorem. The setting under our consideration is a nonstrictly hyperbolic system. our analysis in this article is quite fundamental.展开更多
In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coefficient goes...In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coefficient goes to zero the solutions of the fully viscous equations converges to those of zero viscosity(or zero diffusivity) equations, which extend the previous results on the asymptotic limit under the conditions of the zero parameter(zero viscosity ν = 0 or zero diffusivity η = 0) in 2D case separately.展开更多
We prove that as the viscosity and heat-conductivity coefficients tend to zero, respectively, the global solution of the Navier-Stokes equations for one-dimensional compressible heat-conducting fluids with centered ra...We prove that as the viscosity and heat-conductivity coefficients tend to zero, respectively, the global solution of the Navier-Stokes equations for one-dimensional compressible heat-conducting fluids with centered rarefaction data of small strength converges to the centered rarefaction wave solution of the corresponding Euler equations uniformly away from the initial discontinuity.展开更多
A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to zero.This is particularly important when boundaries are present since vorticitv is typica...A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to zero.This is particularly important when boundaries are present since vorticitv is typically generated at the boundary as a result of boundary layer separation.The boundary laver theory,developed by Prandtl about a hundred years ago,has become a standard tool in addressing these questions.Yet at the mathematical level,there is still a lack of fundamental understanding of these questions and the validity of the boundary layer theory.In this article,we review recent progresses on the analysis of Prandtl’s equation and the related issue of the zero-viscosity limit for the solutions of the Navier-Stokes equation.We also discuss some directions where progress is expected in the near future.展开更多
In this paper, we consider the viscous incompressible magnetohydrodynamic （MHD） system with a new boundary condition for a general smooth domain in R^3. We obtain the well-posedness of the system and the vanishing v...In this paper, we consider the viscous incompressible magnetohydrodynamic （MHD） system with a new boundary condition for a general smooth domain in R^3. We obtain the well-posedness of the system and the vanishing viscosity limit result.展开更多
文摘This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.
基金supported by the National Natural Science Foundation of China(11671319,11931013).
文摘This paper is devoted to studying the zero dissipation limit problem for the one-dimensional compressible Navier-Stokes equations with selected density-dependent viscosity.In particular,we focus our attention on the viscosity taking the formμ(ρ)=ρ^(ϵ)(ϵ>0).For the selected density-dependent viscosity,it is proved that the solutions of the one-dimensional compressible Navier-Stokes equations with centered rarefaction wave initial data exist for all time,and converge to the centered rarefaction waves as the viscosity vanishes,uniformly away from the initial discontinuities.New and subtle analysis is developed to overcome difficulties due to the selected density-dependent viscosity to derive energy estimates,in addition to the scaling argument and elementary energy analysis.Moreover,our results extend the studies in[Xin Z P.Comm Pure Appl Math,1993,46(5):621-665].
文摘In this paper we have obtained the existence of weak solutions of the small disturbance equations of steady two-dimension flow [GRAPHICS] with Riemann date [GRAPHICS] where v+ greater-than-or-equal-to 0, v- greater-than-or-equal-to 0 and u- less-than-or-equal-to u+ by introducing 'artificial' viscosity terms and employing Helley's theorem. The setting under our consideration is a nonstrictly hyperbolic system. our analysis in this article is quite fundamental.
基金Supported by the Youth Science Fund for Disaster Prevention and Reduction(201207)Supported by the Teachers’Scientific Research Fund of China Earthquake Administration(20140109)
文摘In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coefficient goes to zero the solutions of the fully viscous equations converges to those of zero viscosity(or zero diffusivity) equations, which extend the previous results on the asymptotic limit under the conditions of the zero parameter(zero viscosity ν = 0 or zero diffusivity η = 0) in 2D case separately.
文摘We prove that as the viscosity and heat-conductivity coefficients tend to zero, respectively, the global solution of the Navier-Stokes equations for one-dimensional compressible heat-conducting fluids with centered rarefaction data of small strength converges to the centered rarefaction wave solution of the corresponding Euler equations uniformly away from the initial discontinuity.
文摘A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to zero.This is particularly important when boundaries are present since vorticitv is typically generated at the boundary as a result of boundary layer separation.The boundary laver theory,developed by Prandtl about a hundred years ago,has become a standard tool in addressing these questions.Yet at the mathematical level,there is still a lack of fundamental understanding of these questions and the validity of the boundary layer theory.In this article,we review recent progresses on the analysis of Prandtl’s equation and the related issue of the zero-viscosity limit for the solutions of the Navier-Stokes equation.We also discuss some directions where progress is expected in the near future.
基金The authors were partially supported by the National Natural Science Foundation of China （No.11371042）.
文摘In this paper, we consider the viscous incompressible magnetohydrodynamic （MHD） system with a new boundary condition for a general smooth domain in R^3. We obtain the well-posedness of the system and the vanishing viscosity limit result.
