Ill-Posedness of Leray Solutions for the Hypodissipative Navier-Stokes Equations
Ill-Posedness of Leray Solutions for the Hypodissipative Navier-Stokes Equations
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DOI：
10.1007/s00220-018-3177-x
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发表时间：
2018-09-01
影响因子：
2.4
通讯作者：
De Rosa, Luigi
中科院分区：
文献类型：
--
作者：
Colombo, Maria;De Lellis, Camillo;De Rosa, Luigi
证明了当耗散项为指数分数阶Laplacian时，亚耗散Navier-Stokes方程Cauchy问题的Leray解的不适定性。证明遵循“凸积分方法”介绍的第二作者和Laszl Sz，kelyhidi Jr。不可压缩的欧拉方程。这些方法甚至对[1/5，1/2]范围内的指数也确实产生了一些结论。
We prove the ill-posedness of Leray solutions to the Cauchy problem for the hypodissipative Navier-Stokes equations, when the dissipative term is a fractional Laplacian with exponent . The proof follows the "convex integration methods" introduced by the second author and Laszl Sz,kelyhidi Jr. for the incompressible Euler equations. The methods yield indeed some conclusions even for exponents in the range [1/5, 1/2].