Gain of Regularity for the KP-I Equation

Julie Levandosky (1) , Mauricio Sepulveda (2) , Octavio Vera (3)

1 Mathematics Department
2 DIM - Departamento de Ingeniería Matemática [Santiago]
3 Departamento de Matematicas

In this paper we study the smoothness properties of solutions to the KP-I equation. We show that the equation's dispersive nature leads to a gain in regularity for the solution. In particular, if the initial data $\phi$ possesses certain regularity and sufficient decay as $x \rightarrow \infty$, then the solution $u(t)$ will be smoother than $\phi$ for $0 < t \leq T$ where $T$ is the existence time of the solution.

Mots clés: KP-I equation; gain in regularity; weighted Sobolev space.; weighted Sobolev space

Domaines: Equations aux dérivées partielles [math.AP]

Julie Levandosky, Mauricio Sepulveda, Octavio Vera. Gain of Regularity for the KP-I Equation. Journal of Differential Equations, 2008, 245 (3), pp.762-808. ⟨10.1016/j.jde.2008.01.016⟩. ⟨hal-00167133⟩