Communications in Partial Differential Equations · 2001 · 74 citations · 8 references
Natural SciencesMathematicsDifferential EquationsFinite Element AnalysisFinite Element MethodsBoundary ConditionsBoundary-value ProblemsInitial Value ProblemsPartial Differential EquationsWeak FormulationCauchy ProblemGlobal Well-posednessIll-posed ProblemsLocal Well-posednessSobolev Spaces
It is proved that the Cauchy problem for the Kadomtsev-Petviashvili II (KPII) equation is locally well posed in the anisotropic Sobolev spaces H s 1 s 2 (R 2) with s 1 > −⅓ and s 2 ≥ 0, and globally well posed in H s 10(R 2) with s 1 > −.
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