Duke Mathematical Journal · 2002 · 125 citations · 16 references
Natural SciencesMathematicsComputational Fluid DynamicsDifferential EquationsFluid DynamicsBoundary-value ProblemsInitial Value ProblemsIntegral EquationsIterative SolversNumerical Methods For Differential EquationsPartial Differential EquationsCauchy ProblemIll-posed Integral EquationsIll-posed ProblemsIll-posedness AnalysisPicard IterationSobolev Spaces
The main results of this paper are concerned with the "bad" behavior of the KP-I equation with respect to a Picard iteration scheme applied to the associated integral equation, for data in usual or anisotropic Sobolev spaces. This leads to some kind of ill-posedness of the corresponding Cauchy problem: the flow map cannot be of class $C\sp 2$ in any Sobolev space.
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