The inviscid limit for the 2D Navier-Stokes equations in bounded domains
The inviscid limit for the 2D Navier-Stokes equations in bounded domains
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DOI：
10.3934/krm.2022004
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发表时间：
2021-11
影响因子：
1
通讯作者：
C. Bardos;Trinh T. Nguyen;Toan T. Nguyen;E. Titi
中科院分区：
文献类型：
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作者：
C. Bardos;Trinh T. Nguyen;Toan T. Nguyen;E. Titi
我们证明了无粘极限的不可压缩Navier-Stokes方程的数据，分析只有在边界附近的一般二维有界域。我们的证明是直接的，使用的涡度制定与非局部边界条件，显式半群的线性Stokes问题的扁平边界附近，和标准的适定性理论的Navier-Stokes方程在Sobolev空间远离边界。
We prove the inviscid limit for the incompressible Navier-Stokes equations for data that are analytic only near the boundary in a general two-dimensional bounded domain. Our proof is direct, using the vorticity formulation with a nonlocal boundary condition, the explicit semigroup of the linear Stokes problem near the flatten boundary, and the standard wellposedness theory of Navier-Stokes equations in Sobolev spaces away from the boundary.