Continuity of the data-to-solution map for the FORQ equation in Besov\n Spaces

2020/10/09 by John Holmes, Holmes, John, Feride Tığlay +4 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2010.04612

openalex publication_date 2020/10/09 · openalex created_date 2023/01/02 · openalex updated_date 2026/07/28

Abstract

For Besov spaces B^s_p,r( rr) with s>\max 2 + frac1p , frac52 ,\np \∈ (1,\∞] and r \∈ [1 , \∞), it is proved that the\ndata-to-solution map for the FORQ equation is not uniformly continuous from\nB^s_p,r( rr) to C([0,T]; B^s_p,r( rr)). The proof of non-uniform\ndependence is based on approximate solutions and the Littlewood-Paley\ndecomposition.\n

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