Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations

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 a...

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Veröffentlicht in:	Archive for rational mechanics and analysis 2016-09, Vol.221 (3), p.1317-1344
Hauptverfasser:	Han-Kwan, Daniel, Nguyen, Toan T.
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis of PDEs Archives Classical Mechanics Complex Systems Euler equations Euler-Lagrange equation Eulers equations Fluid- and Aerodynamics Hydrostatics Mathematical analysis Mathematical and Computational Physics Mathematics Physics Physics and Astronomy Spectra Theoretical Vlasov equations
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Zusammenfassung:	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.
ISSN:	0003-9527 1432-0673
DOI:	10.1007/s00205-016-0985-z