Remarks on the inviscid limit problem for the Navier-Stokes equations
Remarks on the inviscid limit problem for the Navier-Stokes equations
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发表时间：
2020
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通讯作者：
I. Kukavica;V. Vicol;Fei Wang
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作者：
I. Kukavica;V. Vicol;Fei Wang
对于仅在边界附近解析的数据，我们证明了在无粘极限下Navier-Stokes解收敛到相应的Euler解。与以前的结果相比，在本文中，我们只需要一个可积的解析范数的初始数据，相对于正常变量的有界性，从而消除了统一的粘性有界性假设的涡度。因此，我们可以允许初始涡量在接近集合y = 0的地方是无界的，我们把这个集合作为区域的边界;特别地，对于任何δ> 0，当y接近0时，涡量可以以1/y的速率增长。2020年9月20日
For data which are analytic only close to the boundary of the domain, we prove that in the inviscid limit the Navier-Stokes solution converges to the corresponding Euler solution. Compared to earlier results, in this paper we only require boundedness of an integrable analytic norm of the initial data, with respect to the normal variable, thus removing the uniform in viscosity boundedness assumption on the vorticity. As a consequence, we may allow the initial vorticity to be unbounded close to the set y = 0, which we take as the boundary of the domain; in particular the vorticity can grow with the rate 1/y for y close to 0, for any δ > 0. September 20, 2020