A smoothing effect and polynomial growth of the Sobolev norms for the KP-II equation

DOI10.1016/j.jde.2004.10.002zbMath1081.35097OpenAlexW2038150153MaRDI QIDQ2576889

Nickolay Tzvetkov, Pedro Isaza J., Jorge Mejía L.

Publication date: 29 December 2005

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2004.10.002

zbMATH Keywords

Fourier transformintegral equationwell-posednessglobal solutionsnonlinear dispersive equationsanisotropic Sobolev spaces

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (8)

Dynamics of solitary waves and periodic waves for a generalized KP-MEW-Burgers equation with damping ⋮ Nonlinear smoothing for dispersive PDE: a unified approach ⋮ Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations ⋮ The Cauchy problem for the rotation-modified Kadomtsev-Petviashvili type equation ⋮ The Cauchy problem for a two-dimensional generalized Kadomtsev–Petviashvili-I equation in anisotropic Sobolev spaces ⋮ Nonlinear smoothing and unconditional uniqueness for the Benjamin-Ono equation in weighted Sobolev spaces ⋮ Polynomial growth of high Sobolev norms of solutions to the Zakharov-Kuznetsov equation ⋮ Existence results of solitary wave solutions for a delayed Camassa-Holm-KP equation

Cites Work

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• On the growth of high Sobolev norms of solutions for KdV and Schrödinger equations
• Degenerative dispersion laws, motion invariants and kinetic equations
• On the Cauchy problem for the Kadomtsev-Petviashvili equation
• Global well-posedness for the KP-I equation
• LOCAL AND GLOBAL CAUCHY PROBLEMS FOR THE KADOMTSEV–PETVIASHVILI (KP–II) EQUATION IN SOBOLEV SPACES OF NEGATIVE INDICES
• Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
• Global low-regularity solutions for Kadomtsev-Petviashvili equation

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