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Lower bounds for derivatives of solutions for nonlinear Schrödinger equations

Published online by Cambridge University Press:  25 March 2009

Andrei Biryuk
Andrei Biryuk
Affiliation:
Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de Matematica, Instituto Superior Técnico, Av. Rovisco Pais, 049-001 Lisboa, Portugal (abiryuk@math.ist.utl.pt)
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Abstract

The main goal of this paper is to obtain the lower bounds

for solutions uν of nonlinear Schrödinger equations with small viscosity ν. We also discuss the application of the above estimate to the theory of turbulence. Namely, we are interested in time-averaged lower bounds, which are important in establishing upper bounds for the turbulent space-scale.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 2 , April 2009 , pp. 237 - 251
Copyright
Copyright © Royal Society of Edinburgh 2009

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