Intermediate long wave equation in negative Sobolev spaces

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Ill-posed problems for PDEs (35R25) A priori estimates in context of PDEs (35B45) Internal waves for incompressible inviscid fluids (76B55)

Cites Work

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Improvement of the energy method for strongly nonresonant dispersive equations and applications
Nonlocal models for nonlinear, dispersive waves
On the exact solutions of the intermediate long-wave equation
On well-posedness for some dispersive perturbations of Burgers' equation
On the ill-posedness of some canonical dispersive equations.
Energy and local energy bounds for the 1-d cubic NLS equation in \(H^{-\frac{1}{4}}\)
The Cauchy problem for the Benjamin-Ono equation in \(L^{2}\) revisited
Global well-posedness of the one-dimensional cubic nonlinear Schrödinger equation in almost critical spaces
Low regularity conservation laws for the Benjamin-Ono equation
Nonlinear dispersive equations. Inverse scattering and PDE methods
KdV is well-posed in \(H^{-1}\)
Low regularity conservation laws for integrable PDE
Global well-posedness for \(H^{-1}(\mathbb{R})\) perturbations of KdV with exotic spatial asymptotics
Ill-posedness for the derivative Schrödinger and generalized Benjamin-Ono equations
Ill-Posedness Issues for the Benjamin--Ono and Related Equations
Global well-posedness of the Benjamin–Ono equation in low-regularity spaces
Global well-posedness in <i>L</i><sup xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> for the periodic Benjamin-Ono equation
Lagrange multiplier formalism for a spin-3/2 field
On periodic and solitary wavelike solutions of the intermediate long-wave equation
GLOBAL WELL-POSEDNESS OF THE PERIODIC CUBIC FOURTH ORDER NLS IN NEGATIVE SOBOLEV SPACES
Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation
Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE
A Priori Estimates for the Derivative Nonlinear Schrödinger Equation
Sharp well-posedness results of the Benjamin-Ono equation in \(H^s(\mathbb{T},\mathbb{R})\) and qualitative properties of its solutions
Deep-water and shallow-water limits of the intermediate long wave equation
Sharp well-posedness for the Benjamin--Ono equation

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