In this paper, the Dirichlet problem of Stokes approximate of non-homogeneous incompressible Navier-Stokes equations is studied. It is shown that there exist global weak solutions as well as global and unique strong s...In this paper, the Dirichlet problem of Stokes approximate of non-homogeneous incompressible Navier-Stokes equations is studied. It is shown that there exist global weak solutions as well as global and unique strong solution for this problem, under the assumption that initial density po（x） is bounded away from 0 and other appropriate assumptions （see Theorem 1 and Theorem 2）. The semi-Galerkin method is applied to construct the approximate solutions and a prior estimates are made to elaborate upon the compactness of the approximate solutions.展开更多
The main purpose of this paper is to prove the well-posedness of the two-dimensional Boussinesq equations when the initial vorticity wo C L^1 （R^2） （or the finite Radon measure space）. Using the stream function fo...The main purpose of this paper is to prove the well-posedness of the two-dimensional Boussinesq equations when the initial vorticity wo C L^1 （R^2） （or the finite Radon measure space）. Using the stream function form of the equations and the Schauder fixed-point theorem to get the new proof of these results, we get that when the initial vorticity is smooth, there exists a unique classical solutions for the Cauchy problem of the two dimensional Boussinesq equations.展开更多
In this paper,we study the Cauchy problem for the 3D generalized Navier-Stokes-Boussinesq equations with fractional diffusion：{ut＋（u·▽）u＋v∧^2αu=-▽p＋θe3,e3=（0,0,1）^T,θt＋（u·▽）θ=0,Dicu=0. Wit...In this paper,we study the Cauchy problem for the 3D generalized Navier-Stokes-Boussinesq equations with fractional diffusion：{ut＋（u·▽）u＋v∧^2αu=-▽p＋θe3,e3=（0,0,1）^T,θt＋（u·▽）θ=0,Dicu=0. With the help of the smoothing effect of the fractional diffusion operator and a logarithmic estimate,we prove the global well-posedness for this system with α≥5/4.Moreover,the uniqueness and continuity of the solution with weaker initial data is based on Fourier localization technique.Our results extend ones on the 3D Navier-Stokes equations with fractional diffusion.展开更多
基金the National Natural Science Foundation of China(No.10431060)
文摘In this paper, the Dirichlet problem of Stokes approximate of non-homogeneous incompressible Navier-Stokes equations is studied. It is shown that there exist global weak solutions as well as global and unique strong solution for this problem, under the assumption that initial density po（x） is bounded away from 0 and other appropriate assumptions （see Theorem 1 and Theorem 2）. The semi-Galerkin method is applied to construct the approximate solutions and a prior estimates are made to elaborate upon the compactness of the approximate solutions.
基金supported by the National Natural Science Foundation of China (No. 11171229)supported by 973 program (Grant No. 2011CB711100)
文摘The main purpose of this paper is to prove the well-posedness of the two-dimensional Boussinesq equations when the initial vorticity wo C L^1 （R^2） （or the finite Radon measure space）. Using the stream function form of the equations and the Schauder fixed-point theorem to get the new proof of these results, we get that when the initial vorticity is smooth, there exists a unique classical solutions for the Cauchy problem of the two dimensional Boussinesq equations.
基金supported by National Natural Sciences Foundation of China(No.11171229,11231006 and 11228102)project of Beijing Chang Chen Xue Zhe
文摘In this paper,we study the Cauchy problem for the 3D generalized Navier-Stokes-Boussinesq equations with fractional diffusion：{ut＋（u·▽）u＋v∧^2αu=-▽p＋θe3,e3=（0,0,1）^T,θt＋（u·▽）θ=0,Dicu=0. With the help of the smoothing effect of the fractional diffusion operator and a logarithmic estimate,we prove the global well-posedness for this system with α≥5/4.Moreover,the uniqueness and continuity of the solution with weaker initial data is based on Fourier localization technique.Our results extend ones on the 3D Navier-Stokes equations with fractional diffusion.
