Ill-posedness of the incompressible magneto-hydrodynamics system in B_∞,∞^-1

2012/11/16 by Dai, Mimi
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1211.3972

Abstract

We demonstrate that the three dimensional incompressible magneto-hydrodynamics (MHD) system is ill-posed in the largest scaling invariant space B_∞,∞^-1. The construction method of initial data used in this paper is different from the one in a previous work [DQS] of the author. Specifically, we construct initial data which has finite energy and is small enough in H^s∩ B_∞,∞^-1, with s<1/2, such that any Leray-Hopf type of weak solution to the MHD system starting from this initial data is discontinuous at time t=0 in the metric of B_∞,∞^-1.

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