Global low-regularity solutions for Kadomtsev-Petviashvili equation

zbMath0977.35125MaRDI QIDQ5933754

Nickolay Tzvetkov

Publication date: 14 June 2001

Published in: Differential and Integral Equations (Search for Journal in Brave)

zbMATH Keywords

existenceinitial value problemglobal solutionsKP-II equationnonsmooth data

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) KdV equations (Korteweg-de Vries equations) (35Q53) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45)

Related Items (21)

Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋 ⋮ Stability of line solitons for the KP-II equation in ℝ² ⋮ 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 ⋮ Linear stability of elastic 2-line solitons for the KP-II equation ⋮ Existence and concentration of nontrivial solitary waves for a generalized Kadomtsev-Petviashvili equation in \(\mathbb{R}^2\) ⋮ The Cauchy problem for a two-dimensional generalized Kadomtsev–Petviashvili-I equation in anisotropic Sobolev spaces ⋮ The Phase Shift of Line Solitons for the KP-II Equation ⋮ Global well-posedness for the KP-II equation on the background of a non-localized solution ⋮ Well-posedness for the Kadomtsev-Petviashvili II equation and generalisations ⋮ Global well-posedness for the KP-I equation on the background of a non-localized solution ⋮ Stability of the line soliton of the KP-II equation under periodic transverse perturbations ⋮ LOCAL AND GLOBAL CAUCHY PROBLEMS FOR THE KADOMTSEV–PETVIASHVILI (KP–II) EQUATION IN SOBOLEV SPACES OF NEGATIVE INDICES ⋮ On the local and global well-posedness theory for the KP-I equation ⋮ On the Propagation of Regularity of Solutions of the Kadomtsev--Petviashvili Equation ⋮ On a model system for the oblique interaction of internal gravity waves ⋮ Multiple solitary waves for a generalized Kadomtsev-Petviashvili equation with a potential ⋮ On the propagation of regularities in solutions of the fifth order Kadomtsev-Petviashvili II equation ⋮ Sharp well-posedness of the Cauchy problem for the rotation-modified Kadomtsev-Petviashvili equation in anisotropic Sobolev spaces ⋮ Local regularity and decay estimates of solitary waves for the rotation-modified Kadomtsev-Petviashvili equation ⋮ A smoothing effect and polynomial growth of the Sobolev norms for the KP-II equation

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