Cubic Nonlinear Schrödinger Equation on Three Dimensional Balls with Radial Data

DOI10.1080/03605300802402591zbMath1157.35101arXivmath/0608689OpenAlexW2000036705MaRDI QIDQ3603838

Ramona Anton

Publication date: 19 February 2009

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0608689

zbMATH Keywords

nonlinear Schrödinger equationzeros of Bessel functions\(X^{s,b}\) spacesbilinear Strichartz estimate

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (8)

Global well-posedness for the cubic fractional NLS on the unit disk ⋮ Local controllability of 1D linear and nonlinear Schrödinger equations with bilinear control ⋮ Local and global well-posedness for a quadratic Schrödinger system on Zoll manifolds ⋮ On the cubic NLS on 3D compact domains ⋮ Global regularity for the energy-critical NLS on \(\mathbb S^3\) ⋮ Local well-posedness for the quadratic Schrödinger equation in two-dimensional compact manifolds with boundary ⋮ WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity ⋮ Global well-posedness and long-time behavior of the fractional NLS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces
• Existence of solutions for Schrödinger evolution equations
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Exponential sums and nonlinear Schrödinger equations
• Two singular dynamics of the nonlinear Schrödinger equation on a plane domain
• Finite energy solutions of the Yang-Mills equations in \(\mathbb{R}^{3+1}\)
• Multilinear weighted convolution of L 2 functions, and applications to nonlinear dispersive equations
• STRICHARTZ ESTIMATES FOR A SCHRÖDINGER OPERATOR WITH NONSMOOTH COEFFICIENTS
• On smooth solutions to the initial-boundary value problem for the nonlinear schrödinger equation in two space dimensions
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Nonlinear Schrödinger evolution equations
• Endpoint Strichartz estimates
• Strichartz inequalities and the nonlinear Schrodinger equation on compact manifolds
• Some recent results on the zeros of Bessel functions and orthogonal polynomials

This page was built for publication: Cubic Nonlinear Schrödinger Equation on Three Dimensional Balls with Radial Data