Continuity of the data-to-solution map for the FORQ equation in Besov Spaces
Abstract
For Besov spaces Bsp,r() with s>\ 2 + 1p , 52\ , p ∈ (1,∞] and r ∈ [1 , ∞), it is proved that the data-to-solution map for the FORQ equation is not uniformly continuous from Bsp,r() to C([0,T]; Bsp,r()). The proof of non-uniform dependence is based on approximate solutions and the Littlewood-Paley decomposition.
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