Ill-posedness of the hydrostatic Euler and singular Vlasov equations

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.

References in corpus (2)

• Quasineutral limit for Vlasov-Poisson via Wasserstein stability estimates in higher dimension
• Nonlinear instability of Vlasov-Maxwell systems in the classical and quasineutral limits

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