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arXiv · 1507.01813

Ill-posedness of the hydrostatic Euler and singular Vlasov equations

Daniel Han-Kwan·Toan T. Nguyen
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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 it 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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Daniel Han-Kwan, Toan T. Nguyen. 2016-02-11. Ill-posedness of the hydrostatic Euler and singular Vlasov equations. https://doi.org/10.1007/s00205-016-0985-z

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