Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations

被引：38

作者：

Han-Kwan, Daniel ^{[1
]}

Nguyen, Toan T. ^{[2
]}

机构：

[1] Univ Paris Saclay, CNRS, Ecole Polytech, CMLS, F-91128 Palaiseau, France

[2] Penn State Univ, Dept Math, State Coll, PA 16802 USA

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2016年 / 221卷 / 03期

关键词：

QUASI-NEUTRAL LIMIT; POISSON SYSTEM; PRANDTL EQUATION; LOCAL EXISTENCE; WELL-POSEDNESS; CAUCHY-PROBLEM; INSTABILITY; DERIVATION; ISSUES; DOMAIN;

D O I：

10.1007/s00205-016-0985-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we develop an abstract framework to establish ill-posedness, in the sense of Hadamard, for some nonlocal PDEs displaying unbounded unstable spectra. We apply this to prove the ill-posedness for the hydrostatic Euler equations as well as for the kinetic incompressible Euler equations and the Vlasov-Dirac-Benney system.

引用

页码：1317 / 1344

页数：28

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