In this article, we prove the existence and uniqueness of solutions of the NavierStokes equations with Navier slip boundary condition for incompressible fluid in a bounded domain of R^3. The results are established by...In this article, we prove the existence and uniqueness of solutions of the NavierStokes equations with Navier slip boundary condition for incompressible fluid in a bounded domain of R^3. The results are established by the Galerkin approximation method and improved the existing results.展开更多
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditi...We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition （without the incompressibility condition）, which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n（n ≥ 3） with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.展开更多
An analytical approximation for the similarity solutions of the two-and three-dimensional stagnation slip flow and heat transfer is obtained by using the homotopy analysis method. This method is a series expansion met...An analytical approximation for the similarity solutions of the two-and three-dimensional stagnation slip flow and heat transfer is obtained by using the homotopy analysis method. This method is a series expansion method, but it is different from the perturbation technique, because it is independent of small physical parameters at all. Instead, it is based on a continuous mapping in topology so that it is applicable for not only weakly but also strongly nonlinear flow phenomena. Convergent [m,m] homotopy Padé approximants are obtained and compared with the numerical results and the asymptotic approximations. It is found that the homotopy Padé approximants agree well with the numerical results. The effects of the slip length and the thermal slip constant β on the heat transfer characteristics are investigated and discussed.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
基金supported by National Board for Higher Mathematics(02011/9/2019NBHM(R.P.)/R and D Ⅱ/1324)
文摘In this article, we prove the existence and uniqueness of solutions of the NavierStokes equations with Navier slip boundary condition for incompressible fluid in a bounded domain of R^3. The results are established by the Galerkin approximation method and improved the existing results.
基金supported in part by the National Science Foundation under Grants DMS-0807551, DMS-0720925, and DMS-0505473the Natural Science Foundationof China (10728101)supported in part by EPSRC grant EP/F029578/1
文摘We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition （without the incompressibility condition）, which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n（n ≥ 3） with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.
基金Supported by the National Natural Science Foundation of China (Grant No.10872129)
文摘An analytical approximation for the similarity solutions of the two-and three-dimensional stagnation slip flow and heat transfer is obtained by using the homotopy analysis method. This method is a series expansion method, but it is different from the perturbation technique, because it is independent of small physical parameters at all. Instead, it is based on a continuous mapping in topology so that it is applicable for not only weakly but also strongly nonlinear flow phenomena. Convergent [m,m] homotopy Padé approximants are obtained and compared with the numerical results and the asymptotic approximations. It is found that the homotopy Padé approximants agree well with the numerical results. The effects of the slip length and the thermal slip constant β on the heat transfer characteristics are investigated and discussed.
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.
