Oscillatory integral estimates and global well-posedness for the 2D Boussinesq equation

DOI10.1007/s00574-012-0031-1zbMath1257.35164OpenAlexW1989235544MaRDI QIDQ1928350

Frédéric Rousset, Luiz Gustavo Farah, Nickolay Tzvetkov

Publication date: 3 January 2013

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00574-012-0031-1

zbMATH Keywords

global well-posedness2D Boussinesq equationmultidimensional oscillatory integral

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (3)

Random Data Wave Equations ⋮ A stationary phase type estimate ⋮ On the linearized Vlasov-Poisson system on the whole space around stable homogeneous equilibria

Cites Work

• Local well-posedness for quadratic nonlinear Schrödinger equations and the ``good Boussinesq equation.
• Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Global existence of small solutions for a generalized Boussinesq equation
• Global well-posedness for the KP-I equation on the background of a non-localized solution
• Transverse nonlinear instability of solitary waves for some Hamiltonian PDE's
• Local Solutions in Sobolev Spaces with Negative Indices for the “Good” Boussinesq Equation
• A Two-dimensional Boussinesq equation for water waves and some of its solutions
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