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MASS CONCENTRATION WITH MIXED NORM FOR A NONELLIPTIC SCHRÖDINGER EQUATION

Part of: Harmonic analysis in several variables Equations of mathematical physics and other areas of application Partial differential equations

Published online by Cambridge University Press:  07 March 2013

SEHEON HAM
SEHEON HAM*
Affiliation:
Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Korea email [email protected]
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Abstract

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This paper is concerned with a mass concentration phenomenon for a two-dimensional nonelliptic Schrödinger equation. It is well known that this phenomenon occurs when the ${L}^{4} $-norm of the solution blows up in finite time. We extend this result to the case where a mixed norm of the solution blows up in finite time.

Keywords

Schrödinger equationrestriction theoremmass concentration

MSC classification

Secondary: 42B37: Harmonic analysis and PDE 35B30: Dependence of solutions on initial and boundary data, parameters 35Q55: NLS-like equations (nonlinear Schrödinger)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 93 , Issue 3 , December 2012 , pp. 238 - 258
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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