Global axisymmetric Euler flows with rotation
Global axisymmetric Euler flows with rotation
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DOI：
10.1007/s00222-022-01145-6
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发表时间：
2021-09
影响因子：
3.1
通讯作者：
Yan Guo;B. Pausader;Klaus Widmayer
中科院分区：
文献类型：
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作者：
Yan Guo;B. Pausader;Klaus Widmayer
我们构造了一类三维Euler方程在均匀刚体转动定态附近的整体动力学解。这些解是轴对称的，具有Sobolev正则性，由于旋转引起的色散效应，具有非零涡旋和线性散射。为了建立这一点，我们引入了一个框架，该框架建立在问题的对称性基础上，并精确地捕获了由于旋转引起的各向异性、色散机制。这使得非线性相互作用的几何形状的精细分析，并允许我们传播尖锐的衰减边界，这是全球欧拉流的建设至关重要的。
We construct a class ofglobal, dynamicalsolutions to the 3dEuler equations near the stationary state given by uniform “rigid body” rotation. These solutions are axisymmetric, of Sobolev regularity, have non-vanishing swirl and scatter linearly, thanks to the dispersive effect induced by the rotation. To establish this, we introduce a framework that builds on the symmetries of the problem and precisely captures the anisotropic, dispersive mechanism due to rotation. This enables a fine analysis of the geometry of nonlinear interactions and allows us to propagate sharp decay bounds, which is crucial for the construction of global Euler flows.