Non Uniqueness of Power-Law Flows

被引：24
作者：
Burczak, Jan [1 ]
Modena, Stefano [2 ]
Szekelyhidi, Laszlo [1 ]
机构：
[1] Univ Leipzig, Inst Math, D-04103 Leipzig, Germany
[2] Tech Univ Darmstadt, Fachbereich Math, D-64285 Darmstadt, Germany
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2021年 / 388卷 / 01期
基金：
欧洲研究理事会;
关键词：
WEAK SOLUTIONS; EULER EQUATIONS; EXISTENCE; FLUIDS; DISSIPATION; REGULARITY; VISCOSITY;
D O I：
10.1007/s00220-021-04231-7
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We apply the technique of convex integration to obtain non-uniqueness and existence results for power-law fluids, in dimension d >= 3. For the power index q below the compactness threshold, i.e. q is an element of (1, 2d/d+2), we show ill-posedness of Leray-Hopf solutions. For a wider class of indices q is an element of (1, 3d+2/d+2) we show ill-posedness of distributional (non-Leray-Hopf) solutions, extending the seminal paper of Buckmaster & Vicol [10]. In this wider class we also construct non-unique solutions for every datum in L-2.
引用
收藏
页码：199 / 243
页数：45
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