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Start Over Author "Blower, Gordon" Topic korteweg-de vries equation Journal stochastics: an international journal of probability & stochastic processes
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1. A logarithmic Sobolev inequality for the invariant measure of the periodic Korteweg–de Vries equation.

Author

Blower, Gordon

Subjects
*SOBOLEV spaces, *KORTEWEG-de Vries equation, *INVARIANT measures, *MATHEMATICAL inequalities, *SCHRODINGER equation, *LOGARITHMIC functions, *PROBABILITY theory
Abstract

The periodic Korteweg–de Vries (KdV) equation arises from a Hamiltonian system with infinite-dimensional phase space . Bourgain has shown that there exists a Gibbs probability measure ν on balls in the phase space such that the Cauchy problem for KdV is well posed on the support of ν, and ν is invariant under the KdV flow. This paper shows that ν satisfies a logarithmic Sobolev inequality. This paper also presents logarithmic Sobolev inequalities for the modified periodic KdV equation and the cubic nonlinear Schrödinger equation, for small values of N. [ABSTRACT FROM AUTHOR]

Published
2012
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