Global solutions and stability properties of the 5th order Gardner equation

2019/01/10 by Alejo, Miguel A., Kwak, Chulkwang
#35Q51 #35Q53 (Primary) #37K10 (Secondary) #37K15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.03350

Abstract

In this work, we deal with the initial value problem of the 5th-order Gardner equation in ℝ, presenting the local well-posedness result in H²(ℝ). As a consequence of the local result, in addition to H²-energy conservation law, we are able to prove the global well-posedness result in H²(ℝ). Finally, we present a stability result for 5th order Gardner breather solution in the Sobolev space H²(ℝ).

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