Periodic Korteweg-de Vries equation with measures as initial data

From MaRDI portal
Publication:1366755

DOI10.1007/s000290050008zbMath0891.35138OpenAlexW2055501279MaRDI QIDQ1366755

Jean Bourgain

Publication date: 19 July 1998

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s000290050008



Related Items

A Note on C^2 Ill-posedness Results for the Zakharov System in Arbitrary Dimension, Global dynamics for the stochastic KdV equation with white noise as initial data, Invariance of the Gibbs measure for the periodic quartic gKdV, On the Work of Jean Bourgain in Nonlinear Dispersive Equations, Low Regularity Local Well-Posedness for the Zero Energy Novikov–Veselov Equation, Invariance of the Gibbs measures for periodic generalized Korteweg-de Vries equations, On the regularization mechanism for the periodic Korteweg-de Vries equation, Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋, Normal form approach to near-linear dynamics of modified KdV equation, Well-posedness and ill-posedness for a fifth-order shallow water wave equation, Ill-posedness results for generalized Boussinesq equations, Periodic cubic hyperbolic Schrödinger equation on \(\mathbb T^2\), The Cauchy problem for quadratic and cubic Ostrovsky equation with negative dispersion, Global wellposedness of KdV in \(H^{-1}(\mathbb T,\mathbb R)\), Symplectic nonsqueezing of the Korteweg-de Vries flow, Remark on the periodic mass critical nonlinear Schrödinger equation, Remark on the semilinear ill-posedness for a periodic higher-order KP-I equation, Local well-posedness for the Zakharov system on the multidimensional torus, Well-posedness for the Cauchy problem associated to the Hirota-Satsuma equation: periodic case, Norm Inflation and Ill-Posedness for the Degasperis-Procesi Equation, Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations in almost critical spaces, Nonhomogeneous boundary value problems for the Korteweg-de Vries equation on a bounded domain, On persistence of spatial analyticity for the dispersion-generalized periodic KdV equation, Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation, Decoupling inequality for paraboloid under shell type restriction and its application to the periodic Zakharov system, Sharp well-posedness of the Cauchy problem for a generalized Ostrovsky equation with positive dispersion, Sparse Optimal Control of the KdV-Burgers Equation on a Bounded Domain, Well-posedness results and dissipative limit of high dimensional KdV-type equations, On the wellposedness of the KdV/KdV2 equations and their frequency maps, Global well-posedness and I method for the fifth order Korteweg-de Vries equation, On the existence of periodic solutions to the modified Korteweg-de Vries equation below \(H^{1/2}(\mathbb{T})\), Global well-posedness for eddy-mean vorticity equations on \(\mathbb{T}^2\), On the one-dimensional cubic nonlinear Schrödinger equation below \(L^{2}\), A refined well-posedness result for the modified KdV equation in the Fourier-Lebesgue spaces, Gevrey regularity of the periodic gKdV equation, The regularized Benjamin-Ono and BBM equations: well-posedness and nonlinear stability, The Hartree and Hartree-Fock equations in Lebesgue \(L^p\) and Fourier-Lebesgue \(\widehat{L}^p\) spaces, Geometric numerical integration. Abstracts from the workshop held March 28 -- April 3, 2021 (hybrid meeting), Sharp ill-posedness results for the KdV and mKdV equations on the torus, Global well-posedness for Schrödinger equation with derivative in \(H^{\frac {1}{2}} (\mathbb R)\), Well-posedness of the stochastic KdV-Burgers equation, Sharp well-posedness for the Benjamin equation, The boson star equation with initial data of low regularity, Globally well and ill posedness for non-elliptic derivative Schrödinger equations with small rough data, Global smoothing for the periodic Benjamin equation in low-regularity spaces, Quadratic dispersive generalized Benjamin-Ono equation, Well-posedness results for the generalized Benjamin-Ono equation with small initial data., On ill-posedness for the generalized BBM equation, Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D, Well-posedness and ill-posedness results for dissipative Benjamin-Ono equations, Well-posedness and ill-posedness of KdV equation with higher dispersion, On the well-posedness of higher order viscous Burgers' equations, Sharp local well-posedness of KdV type equations with dissipative perturbations, On the well-posedness, ill-posedness and norm-inflation for a higher order water wave model on a periodic domain, On the wellposedness of the KdV equation on the space of pseudomeasures, Large dispersion, averaging and attractors: three 1D paradigms, On the Cauchy problem for higher-order nonlinear dispersive equations, Real-valued non-analytic solutions for the generalized Korteweg-de Vries equation, Non-homogeneous boundary value problems for the Korteweg-de Vries and the Korteweg-de Vries-Burgers equations in a quarter plane, Sharp ill-posedness and well-posedness results for the KdV-Burgers equation: The periodic case, General boundary value problems of the Korteweg-de Vries equation on a bounded domain, Ill-posedness of Kawahara equation and Kaup-Kupershmidt equation, The Cauchy problem of a periodic higher order KdV equation in analytic Gevrey spaces, On the ill-posedness for a nonlinear Schrödinger-Airy equation, Global Well-Posedness of mKdV inL2(𝕋, ℝ), The IVP for the evolution equation of wave fronts in chemical reactions in low-regularity Sobolev spaces, The Cauchy problem for higher-order modified Camassa-Holm equations on the circle, Estimates for periodic and Dirichlet eigenvalues of the Schrödinger operator with singular potentials, Almost optimal local well-posedness for improved modified Boussinesq equations, Initial boundary value problem for Korteweg-de Vries equation: a review and open problems, On the invariant measure for the Ostrovsky equation, The Cauchy problem for the Ostrovsky equation with positive dispersion, Local well‐posedness and ill‐posedness for the fractal Burgers equation in homogeneous Sobolev spaces, A remark on the well-posedness of the modified KdV equation in the Fourier-Lebesgue spaces, Ill-posedness of the Navier-Stokes equations in a critical space in 3D, On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data, A Sharp Bilinear Estimate for the Bourgain-Type Space with Application to the Benjamin Equation, Local well-posedness and quantitative ill-posedness for the Ostrovsky equation, The Cauchy problem for a higher order shallow water type equation on the circle, Existence of invariant measures for the stochastic damped KdV equation, Periodic stochastic high-order Degasperis–Procesi equation with cylindrical fBm, Local Solutions in Sobolev Spaces with Negative Indices for the “Good” Boussinesq Equation, Ill-posedness results for the (generalized) Benjamin-Ono-Zakharov-Kuznetsov equation, On the periodic KdV equation in weighted Sobolev spaces, Well-posedness of the modified dispersion-generalized Benjamin-Ono equations in modulation spaces, Multilinear estimates for periodic KdV equations, and applications, On sharp global well-posedness and ill-posedness for a fifth-order KdV-BBM type equation, The Cauchy problem for higher-order KP equations, Well-posedness and weak rotation limit for the Ostrovsky equation, On KP-II type equations on cylinders, Invariance of the white noise for KdV, GLOBAL WELL-POSEDNESS FOR THE KDV EQUATIONS ON THE REAL LINE WITH LOW REGULARITY FORCING TERMS, On the ill-posedness of some canonical dispersive equations., On the work of Jean Bourgain in nonlinear dispersive equations, Bi-infinite solutions for KdV- and Toda-type discrete integrable systems based on path encodings, Local well-posedness for the quantum Zakharov system in three and higher dimensions, Invariance of the Gibbs measure for the Benjamin-Ono equation, Global wellposedness for 1D nonlinear Schrödinger equation for data with an infinite \(L^2\) norm, On the Well-Posedness of the Defocusing mKdV Equation Below $L^{2}$, Global well-posedness for the modified korteweg-de vries equation, Well-posedness and ill-posedness results for the Novikov-Veselov equation



Cites Work