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A logarithmic Sobolev inequality for the invariant measure of the periodic Korteweg–de Vries equation.
- Source :
-
Stochastics: An International Journal of Probability & Stochastic Processes . Aug2012, Vol. 84 Issue 4, p533-542. 10p. - Publication Year :
- 2012
-
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]
Details
- Language :
- English
- ISSN :
- 17442508
- Volume :
- 84
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Stochastics: An International Journal of Probability & Stochastic Processes
- Publication Type :
- Academic Journal
- Accession number :
- 78936445
- Full Text :
- https://doi.org/10.1080/17442508.2011.597860