LOCAL AND GLOBAL CAUCHY PROBLEMS FOR THE KADOMTSEV–PETVIASHVILI (KP–II) EQUATION IN SOBOLEV SPACES OF NEGATIVE INDICES

DOI10.1081/PDE-100002387zbMath0993.35080OpenAlexW2008018511MaRDI QIDQ2747904

Pedro Isaza J., Jorge Mejía L.

Publication date: 29 November 2001

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/pde-100002387

zbMATH Keywords

local wellposednessglobal wellposednessgeneralized Kadomtsev-Petviashvili equation

Mathematics Subject Classification ID

Related Items (37)

Global well-posedness of partially periodic KP-I equation in the energy space and application ⋮ The Cauchy Problem for the Kadomtsev-Petviashvili (KPII) Equation in Three Space Dimensions ⋮ Bilinear space-time estimates for linearised KP-type equations on the three-dimensional torus with applications ⋮ 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 ⋮ Existence, regularity, and concentration phenomenon of nontrivial solitary waves for a class of generalized variable coefficient Kadomtsev-Petviashvili equation ⋮ Well-posedness of the Kadomtsev-Petviashvili-II in the negative Sobolev space with respect to y direction ⋮ The Phase Shift of Line Solitons for the KP-II Equation ⋮ A local well-posed result for the fifth order KP-II initial value problem ⋮ Global well-posedness for the KP-II equation on the background of a non-localized solution ⋮ The direct scattering problem for the perturbed Gr(1, 2) _⩾0 Kadomtsev–Petviash-vili II solitons ⋮ 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 ⋮ Well-posedness of the fifth order Kadomtsev-Petviashvili I equation in anisotropic Sobolev spaces with nonnegative indices ⋮ On the low regularity of the fifth order Kadomtsev-Petviashvili I equation ⋮ Nontrivial solitary waves to the generalized Kadomtsev-Petviashvili equations ⋮ IST Versus PDE: A Comparative Study ⋮ Well-posedness and regularity of the fifth order Kadomtsev-Petviashvili I equation in the analytic Bourgain spaces ⋮ On the Propagation of Regularity of Solutions of the Kadomtsev--Petviashvili Equation ⋮ Well-posedness for the fifth order KP-II initial data problem in \(H^{s, 0}(\mathbb{R} \times \mathbb{T})\) ⋮ Global well-posedness in the energy space for a modified KP II equation via the Miura transform ⋮ Local well-posedness of KP-I initial value problem on torus in the Besov space ⋮ Nontrivial stationary solutions to GKP equation in bounded domain ⋮ Global well-posedness and existence of the global attractor for the Kadomtsev-Petviashvili II equation in the anisotropic Sobolev space ⋮ Multiple solitary waves for a generalized Kadomtsev-Petviashvili equation with a potential ⋮ Solitary waves for a class of generalized Kadomtsev-Petviashvili equation in \(\mathbb{R}^N\) with positive and zero mass ⋮ 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 ⋮ On KP-II type equations on cylinders ⋮ On the high-energy solitary wave solutions for a generalized KP equation in a bounded domain ⋮ A smoothing effect and polynomial growth of the Sobolev norms for the KP-II equation

Cites Work

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• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
• The Cauchy problem for the Kadomtsev-Petviashvili equation (KPII) in Sobolev spaces \(H^s\), \(s>0\).
• On the cauchy problem for kadomtsev-petviashvili equation
• Global low-regularity solutions for Kadomtsev-Petviashvili equation
• Well-posedness for the Kadomtsev-Petviashvili II equation

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