The initial value problem for a class of nonlinear dispersive equations

We consider the initial value problem for a (generalized) equation which arises in the study of propagation of unidirectional nonlinear, dispersive waves. The aim is to study the local and global well-posedness of this problem in classical Sobolev spaces Hs. For the associated linear problem sharp l...

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Bibliographic Details
Main Authors: Kenig, Carlos E., Ponce, Gustavo, Vega, Luis
Format: Book Chapter
Language:English
Subjects:
Initial Value Problem
Nonlinear Dispersive Equation
Schrodinger Equation
Smoothing Effect
Vries Equation
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Summary:We consider the initial value problem for a (generalized) equation which arises in the study of propagation of unidirectional nonlinear, dispersive waves. The aim is to study the local and global well-posedness of this problem in classical Sobolev spaces Hs. For the associated linear problem sharp local and global smoothing effects are proven. It is shown how to use these effects to establish well-posedness result for the nonlinear problem.
ISSN:0075-8434
1617-9692
DOI:10.1007/BFb0084903