Ill-posedness for the derivative Schrödinger and generalized Benjamin-Ono equations
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Publication:2716155
DOI10.1090/S0002-9947-01-02754-4zbMath0970.35154OpenAlexW1826826645MaRDI QIDQ2716155
Felipe Linares, Hebe A. Biagioni
Publication date: 6 June 2001
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0002-9947-01-02754-4
Ill-posed problems for PDEs (35R25) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51)
Related Items (48)
A sufficient condition for global existence of solutions to a generalized derivative nonlinear Schrödinger equation ⋮ The derivative nonlinear Schrödinger equation on the half line ⋮ Stability of solitary waves for derivative nonlinear Schrödinger equation ⋮ Global well-posedness for the derivative nonlinear Schrödinger equation ⋮ On the IVP for the k-Generalized Benjamin–Ono Equation ⋮ Small data well-posedness for derivative nonlinear Schrödinger equations ⋮ Solitary waves for nonlinear Schrödinger equation with derivative ⋮ Stability of solitary waves for a generalized derivative nonlinear Schrödinger equation ⋮ A priori estimates and weak solutions for the derivative nonlinear Schrödinger equation on torus below \(H^{1/2}\) ⋮ Weak continuity of the flow map for the Benjamin-Ono equation on the line ⋮ Optimal small data scattering for the generalized derivative nonlinear Schrödinger equations ⋮ Nonlinear waves and dispersive equations. Abstracts from the workshop held June 26 -- July 2, 2022 ⋮ Unconditional uniqueness for the Benjamin-Ono equation ⋮ On the well-posedness problem for the derivative nonlinear Schrödinger equation ⋮ Refined probabilistic local well-posedness for a cubic Schrödinger half-wave equation ⋮ Growth bound and nonlinear smoothing for the periodic derivative nonlinear Schrödinger equation ⋮ Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS ⋮ Global well-posedness for Schrödinger equation with derivative in \(H^{\frac {1}{2}} (\mathbb R)\) ⋮ On the Cauchy problem for the generalized Benjamin-Ono equation with small initial data. ⋮ On the lifespan of strong solutions to the periodic derivative nonlinear Schrödinger equation ⋮ Invariant measure construction at a fixed mass ⋮ Well-posedness of the generalized Benjamin-Ono-Burgers equations in Sobolev spaces of negative order ⋮ Well-posedness results for the generalized Benjamin-Ono equation with small initial data. ⋮ On a class of solutions to the generalized derivative Schrödinger equations. II ⋮ Instability of solitary wave solutions for the nonlinear Schrödinger equation of derivative type in degenerate case ⋮ The estimates of the ill-posedness index of the (deformed-) continuous Heisenberg spin equation ⋮ Stability of the traveling waves for the derivative Schrödinger equation in the energy space ⋮ On the ill-posedness for a nonlinear Schrödinger-Airy equation ⋮ Energy transfer model for the derivative nonlinear Schrödinger equations on the torus ⋮ Global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition in \(H^{\frac{1}{2}}\) ⋮ Time local well-posedness for the Benjamin-Ono equation with large initial data ⋮ On the stability of periodic waves for the cubic derivative NLS and the quintic NLS ⋮ Orbital stability of solitary waves for generalized derivative nonlinear Schrödinger equations in the endpoint case ⋮ Optimal local well-posedness for the periodic derivative nonlinear Schrödinger equation ⋮ Unconditional uniqueness for the derivative nonlinear Schrödinger equation on the real line ⋮ Local well-posedness for the derivative nonlinear Schrödinger equation with \(L^2\)-subcritical data ⋮ Random data Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity ⋮ Instability of solitary wave solutions for derivative nonlinear Schrödinger equation in endpoint case ⋮ Potential well theory for the derivative nonlinear Schrödinger equation ⋮ Polynomial bound and nonlinear smoothing for the Benjamin-Ono equation on the circle ⋮ Modulational instability of periodic standing waves in the derivative NLS equation ⋮ Microscopic conservation laws for the derivative nonlinear Schrödinger equation ⋮ Ill-posedness results for the (generalized) Benjamin-Ono-Zakharov-Kuznetsov equation ⋮ On a class of solutions to the generalized derivative Schrödinger equations ⋮ Long-period limit of exact periodic traveling wave solutions for the derivative nonlinear Schrödinger equation ⋮ On the Cauchy problem for a nonlocal nonlinear Schrödinger equation ⋮ Global well-posedness and inviscid limit for the generalized Benjamin–Ono–Burgers equation ⋮ Existence and uniqueness of solution for a generalized nonlinear derivative Schrödinger equation
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