The failure of Hölder regularity of solutions for the Euler-Poincaré equations in Besov spaces

2024/02/01 by Qu, Guorong, Li, Min
#35B30 #35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.00456

Abstract

In this paper, we investigate the continuity of solution to the Euler-Poincaré equations. We show that the continuity of the solution cannot be improved to the Hölder continuity. That is, the solution of the Euler-Poincaré equations with initial data u₀∈ B^s_p,r belongs to C([0,T];B^s_p,r(\mathbb R^d)) but not to C^α([0,T];B^s_p,r(\mathbb R^d)) with any α∈(0,1).

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