环形区域中具有非零角速度的径向对称螺旋流的亚声速时间周期解
Subsonic time-periodic solutions to radially symmetric spiral flows in an annulus
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中文总结 AI 辅助
研究环形区域中具有非零角速度的径向对称非等熵欧拉系统的亚声速时间周期解，在特定边界条件下建立其存在性与稳定性，克服导数损失等困难，关键在于重写熵的径向导数及控制扰动积累。
中文摘要 AI 辅助
我们研究环形区域中具有非零角速度的径向对称非等熵欧拉系统的亚声速时间周期解。在边界条件在内圆上耗散而在外圆上非耗散的假设下，我们建立了接近稳态径向对称亚声速螺旋流的时间周期解的存在性和稳定性。值得注意的是，对背景亚声速解没有小量限制。主要困难源于与径向熵导数耦合导致的导数损失以及对角化系统中由非零角速度引起的额外零阶项。分析的关键要素之一是将熵的径向导数重写为沿第一或第四特征方向的导数。另一个是通过适当限制环形区域的宽度来控制沿特征曲线的扰动积累。
英文摘要
We investigate subsonic time-periodic solutions to the radially symmetric non-isentropic Euler system with nonzero angular velocity in an annulus. Under the assumption that the boundary conditions are dissipative on the inner circle and non-dissipative on the outer circle, we establish the existence and stability of time-periodic solutions which are close to steady radially symmetric subsonic spiral flows. It is worth noting that there is no smallness restriction on the background subsonic solutions. The main difficulties arise from the derivative loss caused by the coupling with the radial entropy derivative and the additional zeroth-order terms induced by the nonzero angular velocity in the diagonalized system. One of the key ingredients of the analysis is to rewrite the radial derivative of the entropy as a derivative along the first or fourth characteristic direction. Another one is to control the accumulation of perturbations along characteristic curves by suitably restricting the width of the annulus.
