Uniqueness for the 2-D Euler equations on domains with corners
Uniqueness for the 2-D Euler equations on domains with corners
复制标题
带角域上二维欧拉方程的唯一性
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Chao Wang
中科院分区：
文献类型：
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作者：
C. Lacave;E. Miot;Chao Wang
G 'erard-Varet和Lacave对一类非光滑有界区域，建立了具有有界涡量的二维Euler方程整体弱解的存在性.在尖锐区域的情况下，由于靠近边界的$Delta^{-1}$的不良行为，这种弱解的唯一性问题更加复杂。在目前的工作中，我们证明了唯一性的任何有界和单连通域的角小于$π/2$的有限个。我们的策略依赖于对数Lipschitz型的速度场的规律性。
For a large class of non smooth bounded domains, existence of a global weak solution of the 2D Euler equations, with bounded vorticity, was established by G'erard-Varet and Lacave. In the case of sharp domains, the question of uniqueness for such weak solutions is more involved due to the bad behavior of $Delta^{-1}$ close to the boundary. In the present work, we show uniqueness for any bounded and simply connected domain with a finite number of corners of angles smaller than $pi/2$. Our strategy relies on a log-Lipschitz type regularity for the velocity field.