Low regularity solutions for a 2D quadratic nonlinear Schrödinger equation

DOI10.1090/S0002-9947-08-04415-2zbMath1155.35088arXivmath/0609241OpenAlexW1994804844MaRDI QIDQ3532544

Daniela De Silva, Ioan Bejenaru

Publication date: 28 October 2008

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0609241

zbMATH Keywords

energy estimateslow regularity solutionsbilinear estimatesquadratic nonlinear Schrödinger equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (10)

Ill-posedness for a system of quadratic nonlinear Schrödinger equations in two dimensions ⋮ Low-regularity bilinear estimates for a quadratic nonlinear Schrödinger equation ⋮ Quadratic nonlinear derivative Schrödinger equations - Part 2 ⋮ Higher-order nonlinear Schrödinger equations with singular data ⋮ Critical nonlinear Schrödinger equations with data in homogeneous weighted \(\mathbf L^2\) spaces ⋮ The initial-boundary value problem for the Kawahara equation on the half-line ⋮ A convolution estimate for two-dimensional hypersurfaces ⋮ A nonlinear Schrödinger equation with fractional noise ⋮ Ill-posedness for the nonlinear Schrödinger equation with quadratic non-linearity in low dimensions ⋮ Ill-posedness for the quadratic nonlinear Schrödinger equation with nonlinearity \(|u|^2\)

Cites Work

• Unnamed Item
• Sharp well-posedness and ill-posedness results for a quadratic nonlinear Schrödinger equation
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• On the ill-posedness of some canonical dispersive equations.
• Counterexamples to bilinear estimates related with the KdV equation and the nonlinear Schrödinger equation
• The initial value problem for the 1-D semilinear Schrödinger equation in Besov spaces
• Bilinear estimates and applications to 2d NLS
• Multilinear weighted convolution of L 2 functions, and applications to nonlinear dispersive equations
• Quadratic nonlinear derivative Schrodinger equations. Part I
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Local and global results for wave maps I
• Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
• On the Ill-Posedness of the IVP for the Generalized Korteweg-De Vries and Nonlinear Schrödinger Equations
• Quadratic forms for the 1-D semilinear Schrödinger equation

This page was built for publication: Low regularity solutions for a 2D quadratic nonlinear Schrödinger equation