Large Data Low Regularity Scattering Results for the Wave Equation on the Euclidean Space

DOI10.1080/03605302.2012.736910zbMath1267.35130arXiv1010.2966OpenAlexW2167578951MaRDI QIDQ4916379

Anne-Sophie de Suzzoni

Publication date: 22 April 2013

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

Full work available at URL: https://arxiv.org/abs/1010.2966

zbMATH Keywords

invariant measuresnonlinear wave equationPenrose transform

Mathematics Subject Classification ID

Gaussian processes (60G15) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial value problems for second-order hyperbolic equations (35L15) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Second-order semilinear hyperbolic equations (35L71)

Related Items (11)

Invariance of the Gibbs measure for the periodic quartic gKdV ⋮ Random data final-state problem for the mass-subcritical NLS in $L^2$ ⋮ Random Data Cauchy Theory for Nonlinear Wave Equations of Power-Type on ℝ³ ⋮ Almost sure local wellposedness and scattering for the energy-critical cubic nonlinear Schrödinger equation with supercritical data ⋮ Asymptotic stability of small ground states for NLS under random perturbations ⋮ Consequences of the choice of a particular basis of \(L^2(S^3)\) for the cubic wave equation on the sphere and the Euclidean space ⋮ Almost sure local well-posedness and scattering for the 4D cubic nonlinear Schrödinger equation ⋮ Almost sure scattering for the energy-critical NLS with radial data below H1(R4) ⋮ Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on \(\mathbb R^d\), \(d=4\) and \(5\) ⋮ On the Probabilistic Cauchy Theory for Nonlinear Dispersive PDEs ⋮ On the almost sure scattering for the energy-critical cubic wave equation with supercritical data

Cites Work

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• Random data Cauchy theory for supercritical wave equations. II. A global existence result
• Random data Cauchy theory for supercritical wave equations I: Local theory
• Periodic nonlinear Schrödinger equation and invariant measures
• Invariant measures for the 2D-defocusing nonlinear Schrödinger equation
• Global solutions of nonlinear hyperbolic equations for small initial data
• Strichartz inequalities and the nonlinear Schrodinger equation on compact manifolds
• Maximal functions associated to filtrations

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