Weak solutions for the α-Euler equations and convergence to Euler
Weak solutions for the α-Euler equations and convergence to Euler
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DOI：
10.1088/1361-6544/aa8982
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发表时间：
2016-11
期刊：
影响因子：
1.7
通讯作者：
A. Busuioc;D. Iftimie
中科院分区：
文献类型：
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作者：
A. Busuioc;D. Iftimie
考虑二维有界域上具有Dirichlet边界条件的α-Euler方程的极限Dirichlet 0。假设涡量在Lp中有界，我们证明了整体解的存在性，并证明了具有Lp涡度的不可压缩Euler方程的解的收敛。域可以是多重连通的。我们还讨论了当α和ν都为0时第二级流体的情况。
We consider the limit α→0 for the α-Euler equations in a two-dimensional bounded domain with Dirichlet boundary conditions. Assuming that the vorticity is bounded in Lp, we prove the existence of a global solution and we show the convergence towards a solution of the incompressible Euler equation with Lp vorticity. The domain can be multiply connected. We also discuss the case of the second grade fluid when both α and ν go to 0.