On the unboundedness of higher regularity Sobolev norms of solutions for the critical Schrödinger–Debye system with vanishing relaxation delay

DOI10.1088/1361-6544/30/1/300zbMath1358.35166arXiv1510.02434OpenAlexW2963080248MaRDI QIDQ2958641

Jorge Drumond Silva, Adán J. Corcho

Publication date: 3 February 2017

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.02434

zbMATH Keywords

well-posednessblow-up phenomenaSchödinger-Debye system

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with optics and electromagnetic theory (35Q60) NLS equations (nonlinear Schrödinger equations) (35Q55) Blow-up in context of PDEs (35B44)

Related Items (3)

Scattering theory for the Schrödinger–Debye system ⋮ Thermal effects in short laser pulses: suppression of wave collapse ⋮ On the Cauchy Problem Associated with a Nonequilibrium Bose--Einstein Condensate of Exciton Polaritons

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global well-posedness for the critical Schrödinger-Debye system
• Sharp bilinear estimates and well posedness for the 1-D Schrödinger-Debye system.
• Existence of solitary waves in higher dimensions
• On a class of nonlinear Schrödinger equations. II. Scattering theory, general case
• Blow-up results of virial type for Zakharov equations
• Numerical study of self-focusing solutions to the Schrödinger-Debye system
• Local and global well-posedness for the critical Schrödinger-Debye system
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Endpoint Strichartz estimates
• Self-Focusing in the Perturbed and Unperturbed Nonlinear Schrödinger Equation in Critical Dimension

This page was built for publication: On the unboundedness of higher regularity Sobolev norms of solutions for the critical Schrödinger–Debye system with vanishing relaxation delay