Dynamics of Partial Differential Equations
Volume 13 (2016)
On invariant Gibbs measures for the generalized KdV equations
Pages: 133 – 153
We consider the defocusing generalized KdV equations on the circle. In particular, we construct global-in-time solutions with initial data distributed according to the Gibbs measure and show that the law of the random solutions, at any time, is again given by the Gibbs measure. In handling a nonlinearity of an arbitrary high degree, we make use of the Hermite polynomials and the white noise functional.
generalized KdV equation, Gibbs measure, Hermite polynomial, white noise functional
2010 Mathematics Subject Classification