A sharp condition for the well-posedness of the linear KdV-type equation

DOI10.1090/S0002-9939-2014-12136-8zbMath1303.35086arXiv1209.1658OpenAlexW1972998390MaRDI QIDQ2930630

Timur Akhunov

Publication date: 19 November 2014

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.1658

zbMATH Keywords

energy methodlinearpartial differential equationsdispersiveKdVMizohata condition

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (6)

Well-posedness and ill-posedness for linear fifth-order dispersive equations in the presence of backwards diffusion ⋮ Well-posedness and parabolic smoothing effect for higher order Schrödinger type equations with constant coefficients ⋮ Local well-posedness for a quasilinear Schroedinger equation with degenerate dispersion ⋮ On well-posedness for some Korteweg-de Vries type equations with variable coefficients ⋮ On the generalized nonlinear Camassa-Holm equation ⋮ Well-posedness of fully nonlinear KdV-type evolution equations

Cites Work

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• The Cauchy problem for quasi-linear Schrödinger equations
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• On the Cauchy problem for Schrödinger type equations and the regularity of solutions
• On the wellposed Cauchy problem for some dispersive equations
• Local well-posedness of quasi-linear systems generalizing KdV
• The Initial Value Problem for Third and Fourth Order Dispersive Equations in One Space Dimension
• Microlocal dispersive smoothing for the Schrödinger equation
• Dispersion vs. anti-diffusion: Well-posedness in variable coefficient and quasilinear equations of KdV-type

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