The 'Blow up' problem for a quasilinear Schroedinger equation

Journal Article · Fri Jul 01 00:00:00 EDT 2005 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.1941089· OSTI ID:20699239

Boling, Guo; Jianqing, Chen; Fengqiu, Su ^[1]

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1. Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China)

Consider the blow up results for W{sup 2,2}(R{sup N}) solutions of a quasilinear Schroedinger equation iu{sub t}+{delta}u+{beta} vertical bar u vertical bar {sup p-2}u+{theta}({delta} vertical bar u vertical bar {sup 2})u=0, u{sub /{sub t}=0}}=u{sub 0}(x),x is a member of R{sup N}. When vertical bar x vertical bar u{sub 0} is a member of L{sup 2}(R{sup N}), we show that the W{sup 2,2}(R{sup N}) solutions must blow up for any {beta}{>=}0, {theta} is a member of R and some restriction on p. We also show that the radial symmetric solutions in W{sup 2,2}(R{sup N}) must blow up at finite time without assuming vertical bar x vertical bar u{sub 0} is a member of L{sup 2}(R{sup N})

• OSTI ID: 20699239
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 7 Vol. 46; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
SCHROEDINGER EQUATION
SYMMETRY