The magneto-micropolar equations with periodic boundary conditions: Solution properties at potential blow-up times

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:435

Article

Melo, Wilberclay G.¹ 

[1] Univ Fed Sergipe, Dept Matemat, BR-49100000 Sao Cristovao, SE, Brazil

关键词: Magneto-micropolar equations;    Blow-up criteria;    Homogeneous Sobolev spaces;   

DOI  :  10.1016/j.jmaa.2015.11.005

来源: Elsevier

【 摘 要 】

We examine some estimates involving strong solutions, at potential blow-up times, for the magneto-micropolar equations with periodic boundary conditions. More precisely, if T* < infinity is the first blow-up instant of a solution (u, w, b)(t) defined in the interval [0, T*) and s >= 1/2 + delta, with delta is an element of (0,1), then it holds the inequality parallel to(u, w, b)(t)parallel to((H) over dots) ((T3)) >= C(T* - t)(-(delta s)/(1+2 delta)). In addition, we prove that parallel to(<(u)over cap>, (w) over cap, (b) over cap)parallel to(l1(z3)) >= C(T* - t)(-1/2) in order to obtain as a result the estimate parallel to(u, w, b)(t)parallel to((H) over dots) ((T3)) >= C(T* - t)(-s/3) for s > 3/2. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free