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Title: Continuous properties of the solution map for the Euler equations

In this paper, we study the dependence on initial data of solutions to the incompressible Euler equations in Besov spaces. We show that for s > n/p + 1, p ∈ (1, ∞), and r ∈ [1, ∞], the solution map u{sub 0}↦u is Hölder continuous in Besov space B{sub p,r}{sup s} equipped with weaker topology. When the space variable x is taken to be periodic, we obtain a family of explicit periodic solutions. Furthermore, we prove that for any s∈R and 1 ⩽ r ⩽ ∞, the solution map is not globally uniformly continuous in B{sub 2,r}{sup s}(T{sup n}), which extends some results of Himonas and Misiołek [Commun. Math. Phys. 296(1), 285–301 (2010)].
Authors:
;  [1]
  1. Department of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640 (China)
Publication Date:
OSTI Identifier:
22251070
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EQUATIONS; MAPS; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; PERIODICITY; TOPOLOGY