Well-posedness and stability results for the Gardner equation

Details Well-posedness and stability results for the Gardner equation Well-posedness and stability results for the Gardner equation

2011-10-19

arxiv.org/abs/1110.4211v1

Mathematics

Analysis of PDEs

1 figure. Accepted for publication in Nonlin.Diff Eq.and Appl

Scientific paper

10.1007/s00030-011-0140-3

In this article we present local well-posedness results in the classical Sobolev space H^s(R) with s > 1/4 for the Cauchy problem of the Gardner equation, overcoming the problem of the loss of the scaling property of this equation. We also cover the energy space H^1(R) where global well-posedness follows from the conservation laws of the system. Moreover, we construct solitons of the Gardner equation explicitly and prove that, under certain conditions, this family is orbitally stable in the energy space.

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