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We consider the 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.
|Number of pages||21|
|Journal||Dynamics of Partial Differential Equations|
|Publication status||Published - 23 Jun 2016|
- generalized KdV equation
- Gibbs measure
- Hermite polynomial
- white noise functional
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- 1 Finished
ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
1/03/15 → 29/02/20