A bilinear estimate with applications to the KdV equation
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Publication:4874246
DOI10.1090/S0894-0347-96-00200-7zbMath0848.35114OpenAlexW2170434801MaRDI QIDQ4874246
Gustavo Ponce, Luis Vega, Carlos E. Kenig
Publication date: 24 October 1996
Published in: Journal of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0894-0347-96-00200-7
KdV equations (Korteweg-de Vries equations) (35Q53) Initial value problems for nonlinear higher-order PDEs (35G25) Generalized solutions to partial differential equations (35D99)
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dispersive generalized Benjamin-Ono equation ⋮ Local well-posedness for dispersion generalized Benjamin-Ono equations in Sobolev spaces ⋮ Well-posedness of the Cauchy problem for Ostrovsky, Stepanyants and Tsimring equation with low regularity data ⋮ Control and stabilization of the Korteweg-de Vries equation: recent progresses ⋮ The well posedness of the dissipative Korteweg-de Vries equations with low regularity data ⋮ The local well-posedness for nonlinear fourth-order Schrödinger equation with mass-critical nonlinearity and derivative ⋮ The attractor for the two-dimensional weakly damped KdV equation in belt field ⋮ Inviscid limit behavior of the solution to the one-dimensional generalized Ginzburg-Landau equation ⋮ Random attractors of the stochastic damped forced Ostrovsky equation ⋮ Well-posedness and ill-posedness of KdV equation with higher dispersion ⋮ On the well-posedness of higher order viscous Burgers' equations ⋮ On the local well-posedness for some systems of coupled KdV equations ⋮ Asymptotic stability for KdV solitons in weighted spaces via iteration ⋮ On the Cauchy problem for the generalized shallow water wave equation ⋮ Quadratic forms for a 2-D semilinear Schrödinger equation ⋮ On the growth of high Sobolev norms of solutions for KdV and Schrödinger equations ⋮ Well-posedness of the fifth order Kadomtsev-Petviashvili I equation in anisotropic Sobolev spaces with nonnegative indices ⋮ A note on the Ostrovsky equation in weighted Sobolev spaces ⋮ Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. II. ⋮ Lower bounds on the radius of spatial analyticity for the KdV equation ⋮ The generalized Korteweg-de Vries equation with time oscillating nonlinearity in scale critical Sobolev space ⋮ Non-homogeneous boundary value problems for the Korteweg-de Vries and the Korteweg-de Vries-Burgers equations in a quarter plane ⋮ On the low regularity of the fifth order Kadomtsev-Petviashvili I equation ⋮ Local well-posedness for the dispersion generalized periodic KdV equation ⋮ Well-posedness and stability results for the Gardner equation ⋮ Global existence and asymptotic behavior of solutions to the homogeneous Neumann problem for ILW equation on a half-line ⋮ Smoothing properties for a coupled system of nonlinear evolution dispersive equations ⋮ Ill-posedness of Kawahara equation and Kaup-Kupershmidt equation ⋮ Local analyticity in the time and space variables and the smoothing effect for the fifth-order KdV-type equation ⋮ Global attractor for the weakly damped forced KdV equation in Sobolev spaces of low regularity ⋮ On the periodic Schrödinger-Boussinesq system ⋮ Simple explicit formulae for finite time blow up solutions to the complex KdV equation ⋮ On the well-posedness of the Schrödinger-Korteweg-de Vries system ⋮ Analytic well-posedness of periodic gKdV ⋮ Radius of analyticity and exponential convergence for spectral projections of the generalized KdV equation ⋮ Nearly linear dynamics of nonlinear dispersive waves ⋮ On the invariant measure for the Ostrovsky equation ⋮ The Cauchy problem for the Ostrovsky equation with positive dispersion ⋮ Global well-posedness for the 3D Zakharov-Kuznetsov equation in energy space \(H^1\) ⋮ Well-posedness of a nonlinear boundary value problem for the Korteweg-de Vries equation on a bounded domain ⋮ Existence and regularity of the global attractor for a weakly damped forced shallow water equation in \(H^1(\mathbb R)\) ⋮ Well-posedness of the ADMB-KdV equation in Sobolev spaces of negative indices ⋮ Local and global well-posedness in the energy space for the dissipative Zakharov-Kuznetsov equation in 3D ⋮ Stochastic Korteweg-de Vries equation driven by fractional Brownian motion
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