| Weak and Strong Solutions for the Stokes Approximation of Non-homogeneous Incompressible Navier-Stokes Equations |
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| 作者姓名： | Xiao-jing Cai Quan-sen Jiu Chun-yan Xue |
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| 作者单位： | Xiao-jing Cai~1 Quan-sen Jiu~(1*) Chun-yan Xue~(1，2)1 School of Mathematical Sciences，Capital Normal University，Beijing 100037，China2 Department of Mathematics，Beijing Information Science and Technology University，Beijing 100101，China |
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| 基金项目： | Supported by the National Natural Science Foundation of China （No. 10431060） |
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| 摘 要： | In this paper,the Dirichlet problem of Stokes approximate of non-homogeneous incompressibleNavier-Stokes equations is studied.It is shown that there exist global weak solutions as well as global andunique strong solution for this problem,under the assumption that initial density ρ_0(x)is bounded away from0 and other appropriate assumptions(see Theorem 1 and Theorem 2).The semi-Galerkin method is applied toconstruct the approximate solutions and a prior estimates are made to elaborate upon the compactness of theapproximate solutions.
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| 关 键 词： | 强性溶液 弱性溶液 方程式 数学 |
| 收稿时间： | 8 March 2006 |
| 修稿时间： | 2006-03-08 |
Weak and Strong Solutions for the Stokes Approximation of Non-homogeneous Incompressible Navier-Stokes Equations |
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| Xiao-jing Cai Quan-sen Jiu Chun-yan Xue.Weak and Strong Solutions for the Stokes Approximation of Non-homogeneous Incompressible Navier-Stokes Equations[J].Acta Mathematicae Applicatae Sinica,2007,23(4):637-650. |
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| Authors: | Xiao-jing?Cai Quan-sen?Jiu Chun-yan?Xue |
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| Institution: | (1) School of Mathematical Sciences, Capital Normal University, Beijing, 100037, China;(2) Department of Mathematics, Beijing Information Science and Technology University, Beijing, 100101, China |
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| Abstract: | Abstract
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 ρ0(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.
*Supported by the National Natural Science Foundation of China (No. 10431060) |
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| Keywords: | Non-homogeneous Navier-Stokes equations Stokes approximate weak solutions strong solution |
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