Effect of lower order terms on the well-posedness of Majda-Biello systems

KdV equations (Korteweg-de Vries equations) (35Q53) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial value problems for systems of nonlinear higher-order PDEs (35G55)

Cites Work

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Regularity properties of the cubic nonlinear Schrödinger equation on the half line
Smoothing and global attractors for the Zakharov system on the torus
A note on ill posedness for the KdV equation.
Sharp ill-posedness results for the KdV and mKdV equations on the torus
Global wellposedness of KdV in \(H^{-1}(\mathbb T,\mathbb R)\)
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A model system for strong interaction between internal solitary waves
Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
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Periodic Korteweg-de Vries equation with measures as initial data
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KdV is well-posed in \(H^{-1}\)
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Sur un problème non linéaire
Multilinear weighted convolution of \(L^2\) functions, and applications to nonlinear dispersive equations
Diophantine Conditions in Well-Posedness Theory of Coupled KdV-Type Systems: Local Theory
Weak and Strong Interactions between Internal Solitary Waves
Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
The initial-value problem for the Korteweg-de Vries equation
Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
Weak solvability and well-posedness of a coupled Schrödinger-Korteweg de Vries equation for capillary-gravity wave interactions
Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
A bilinear estimate with applications to the KdV equation
On a model system for the oblique interaction of internal gravity waves

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