Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations

Daniel Han-Kwan; Toan T. Nguyen

doi:10.1007/s00205-016-0985-z

Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations

Daniel Han-Kwan, Toan T. Nguyen

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	1317-1344
Number of pages	28
Journal	Archive for Rational Mechanics and Analysis
Volume	221
Issue number	3
DOIs	https://doi.org/10.1007/s00205-016-0985-z
State	Published - Sep 1 2016

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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abstract = "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.",

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N2 - 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.

AB - 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.

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Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations

Abstract

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