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

2012/11/16 by Mimi Dai, Dai, Mimi
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Compressibility #Computer science #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geometry #Invariant (physics) #Magnetic field #Magnetohydrodynamics #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Navier-Stokes equation solutions #Physics #Quantum mechanics #Scaling #Space (punctuation) #math.AP

paper · pdf · doi:10.48550/arxiv.1211.3972

published in arXiv (Cornell University) (Cornell University) · This paper has been withdrawn due to a scaling error in the initial data construction

openalex publication_date 2012/11/16 · arxiv created 2014/07/25 · arxiv updated 2014/07/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Some mathematical questions related to the mhd equations

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