Non-uniform dependence for the Novikov equation in Besov spaces

2020/02/02 by Jinlu Li, Min Li, Li, Jinlu +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #math.AP

paper · pdf · doi:10.48550/arxiv.2002.00321

arxiv created 2020/02/02 · arxiv updated 2020/02/04

Abstract

In this paper, we investigate the dependence on initial data of solutions to the Novikov equation. We show that the solution map is not uniformly continuous dependence on the initial data in Besov spaces B^s_p,r(\R), s>max\1+\frac 1p,\frac32\.

Citations

• On the ill-posedness of some canonical dispersive equations
• Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation
• Wave breaking for nonlinear nonlocal shallow water equations
• The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations

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• On the well-posedness and non-uniform continuous dependence for the Novikov equation in the Triebel-Lizorkin spaces
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