论文标题
线性可压缩涡流板的各向异性规律性
Anisotropic regularity of linearized compressible vortex sheets
论文作者
论文摘要
我们关注的是在两个空间尺寸中可压缩无粘性流体的Euler方程的超音速涡流板。对于恒定系数的问题，在[10]中，作者得出了一个伪分化方程，该方程描述了涡旋表的不连续性前部的时间演变。与经典稳定性分析一致，如果$ | [v \cdotτ] |> 2 \ sqrt {2} \，c $，问题是弱稳定的，并且在标准加权的Sobolev空间中获得了良好的态度。 本文的目的是通过在功能空间中显示溶液的存在，并在频率空间中具有一些额外的加权各向异性规律性来改善[10]的结果。
We are concerned with supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients, in [10] the authors have derived a pseudo-differential equation which describes the time evolution of the discontinuity front of the vortex sheet. In agreement with the classical stability analysis, the problem is weakly stable if $|[v\cdotτ]|>2\sqrt{2}\,c$, and the well-posedness was obtained in standard weighted Sobolev spaces. The aim of the present paper is to improve the result of [10], by showing the existence of the solution in function spaces with some additional weighted anisotropic regularity in the frequency space.
