论文标题
关于外部域中稳定的平面navier-stokes方程的独特性和非唯一性
On the uniqueness and non-uniqueness of the steady planar Navier-Stokes equations in an exterior domain
论文作者
论文摘要
在本文中，我们研究了外部结构域中具有不同边界条件的稳定平面Navier-Stokes方程的溶液的独特性。对于持续涡度的一类不可压缩流，我们证明了在增强的Navier边界条件下解决方案的独特性。同时，给出了一些反例，以表明解决方案的独特性在Navier边界条件下失败。对于具有Dirichlet边界条件的一般不可压缩流，我们证明了溶液独特性的各种条件。
In this paper we investigate the uniqueness of solutions of the steady planar Navier-Stokes equations with different boundary conditions in the exterior domain. For a class of incompressible flow with constant vorticity, we prove the uniqueness of the solution under the enhanced Navier boundary conditions. At the same time, some counterexamples are given to show that the uniqueness of the solution fails under the Navier boundary conditions. For the general incompressible flow with Dirichlet boundary condition, we prove various sufficient conditions for the uniqueness of the solution.
