A refined well-posedness result for the modified KdV equation in the Fourier-Lebesgue spaces
DOI10.1007/s10884-021-10050-0zbMath1522.35438arXiv2006.15671WikidataQ115383035 ScholiaQ115383035MaRDI QIDQ6174772
Publication date: 17 August 2023
Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2006.15671
Smoothness and regularity of solutions to PDEs (35B65) KdV equations (Korteweg-de Vries equations) (35Q53) Ill-posed problems for PDEs (35R25) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Cites Work
- Unnamed Item
- Unnamed Item
- Invariance of the Gibbs measure for the periodic quartic gKdV
- Sharp ill-posedness results for the KdV and mKdV equations on the torus
- Local well-posedness in low regularity of the mKdV equation with periodic boundary condition
- Periodic stochastic Korteweg-de Vries equation with additive space-time white noise
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
- Multiple-scale perturbation beyond the nonlinear Schrödinger equation. I
- Periodic Korteweg-de Vries equation with measures as initial data
- On the Cauchy problem for the Zakharov system
- Two-dimensional Navier-Stokes equations driven by a space-time white noise
- Invariant measures for the 2D-defocusing nonlinear Schrödinger equation
- Global well-posedness of the one-dimensional cubic nonlinear Schrödinger equation in almost critical spaces
- Optimal local well-posedness for the periodic derivative nonlinear Schrödinger equation
- A remark on the well-posedness of the modified KdV equation in the Fourier-Lebesgue spaces
- Normal form approach to the one-dimensional periodic cubic nonlinear Schrödinger equation in almost critical Fourier-Lebesgue spaces
- On the existence of periodic solutions to the modified Korteweg-de Vries equation below \(H^{1/2}(\mathbb{T})\)
- Normal form approach to unconditional well-posedness of nonlinear dispersive PDEs on the real line
- Low regularity conservation laws for integrable PDE
- On unconditional well-posedness for the periodic modified Korteweg-de Vries equation
- On Unconditional Well-Posedness of Modified KdV
- PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES
- Low Regularity Local Well-Posedness of the Derivative Nonlinear Schrödinger Equation with Periodic Initial Data
- Power series solution of the modified KdV equation
- Local well-posedness for the modified KdV equation in almost critical $\widehat {H^r_s}$-spaces
- Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
- Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
- Non-Existence of Solutions for the Periodic Cubic NLS below ${L}^{{2}}$
- Global Well-Posedness of mKdV inL2(𝕋, ℝ)
- Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
- On the Well-Posedness of the Defocusing mKdV Equation Below $L^{2}$
- On the Cauchy problem for the derivative nonlinear Schrodinger equation with periodic boundary condition
- Exact envelope-soliton solutions of a nonlinear wave equation
- Large-Data Equicontinuity for the Derivative NLS
This page was built for publication: A refined well-posedness result for the modified KdV equation in the Fourier-Lebesgue spaces