Abstract
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 H s. 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.
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Kenig, C.E., Ponce, G., Vega, L. (1990). The initial value problem for a class of nonlinear dispersive equations. In: Fujita, H., Ikebe, T., Kuroda, S.T. (eds) Functional-Analytic Methods for Partial Differential Equations. Lecture Notes in Mathematics, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084903
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DOI: https://doi.org/10.1007/BFb0084903
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