Séminaire Analyse Numérique et EDP
Solutions to the Fifth-Order KP II Equation Scatter
June 2022
Intervenant : Peter Perry
Institution : University of Kentucky
Heure : 15h15 - 16h15
Lieu : 3L8
This is joint work with Camille Schuetz. The fifth-order KP II equation 
$$ \partial_t u + \alpha \partial_x^3 - \partial_x^5 u + u \partial_x u + \partial_x^{-1} \partial_y^2 u = 0 $$
is a two-dimensional generalization of the fifth-order KdV equation (Kawahara equation). Using techniques 
developed by Hadac, Herr, and Koch for the third-order KP II equation, we show that solutions with small initial 
data in the homogeneous Sobolev space $\dot{H}^{-\frac12,0}(\R^2)$ scatter to solutions of the linear equation
$$ \partial_t u + \alpha \partial_x^3 - \partial_x^5 u  + \partial_x^{-1} \partial_y^2 u = 0  $$
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