Quadratic forms for a 2-D semilinear Schrödinger equation
From MaRDI portal
Publication:677111
DOI10.1215/S0012-7094-97-08603-8zbMath0872.35104MaRDI QIDQ677111
Publication date: 15 October 1997
Published in: Duke Mathematical Journal (Search for Journal in Brave)
semilinear Schrödinger equationpolynomial boundLipschitz continuous dependence on the initial function
Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)
Related Items
Local well-posedness for 2-D Schrödinger equation on irrational tori and bounds on Sobolev norms, Low-regularity bilinear estimates for a quadratic nonlinear Schrödinger equation, Sobolev norms explosion for the cubic NLS on irrational tori, Growth of Sobolev norms for the analytic NLS on \(\mathbb{T}^2\), Smoothing and growth bound of periodic generalized Korteweg–De Vries equation, On growth in time of Sobolev norms of smooth solutions of nonlinear Schrödinger equations in \(\mathbb{R}^D\), Full derivation of the wave kinetic equation, Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite gap tori for the 2D cubic NLS equation, Growth bound and nonlinear smoothing for the periodic derivative nonlinear Schrödinger equation, Bilinear estimates and applications to 2d NLS, The growth in time of higher Sobolev norms of solutions to Schrödinger equations on compact Riemannian manifolds, Growth of Sobolev norms in the cubic nonlinear Schrödinger equation with a convolution potential, On the growth of the Sobolev norms for the nonlinear Klein-Gordon equation, A note on growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation, Polynomial bound and nonlinear smoothing for the Benjamin-Ono equation on the circle, Local well-posedness for the quadratic Schrödinger equation in two-dimensional compact manifolds with boundary, Interaction equations for short and long dispersive waves, Global dynamics in nonconservative nonlinear Schrödinger equations, Revisited bilinear Schrödinger estimates with applications to generalized Boussinesq equations, Jubilee volume on the occasion of the 50th year of publication of the journal, On diffusion in high-dimensional Hamiltonian systems and PDE, Asymptotic smoothing effect for a weakly damped nonlinear Schrödinger equation in \(\mathbb{T}^2\), ON THE CAUCHY PROBLEM IN BESOV SPACES FOR A NON-LINEAR SCHRÖDINGER EQUATION
Cites Work
- On the growth of high Sobolev norms of solutions for KdV and Schrödinger equations
- Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
- On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
- On a class of nonlinear Schrödinger equations. II. Scattering theory, general case
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
- The cauchy problem for the critical nonlinear Schrödinger equation in Hs
- A bilinear estimate with applications to the KdV equation
- Quadratic forms for the 1-D semilinear Schrödinger equation
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item