Horizontal Biot-Savart law in general dimension and an application to the 4d magneto-hydrodynamics

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We derive a Biot-Savart law type identity for the horizontal components of the solution to the fluid system of equations with incompressibility in general dimension. Along with another new decomposition of non-linear terms, we give its application to derive two regularity criteria for the four-dimensional magneto-hydrodynamics system, in particular a criteria in terms of two velocity field components, two magnetic field components and two partial derivatives of the other two magnetic field components in a scaling-invariant norm. It is an open problem to obtain a criterion in terms of just two velocity field components and two partial derivatives of two magnetic field components in a scaling-invariant norm; an analogous criterion in the three-dimensional case has already been established.

Original languageEnglish
Pages (from-to)301-328
Number of pages28
JournalDifferential and Integral Equations
Volume31
Issue number3-4
StatePublished - Mar 1 2018

Fingerprint Dive into the research topics of 'Horizontal Biot-Savart law in general dimension and an application to the 4d magneto-hydrodynamics'. Together they form a unique fingerprint.

Cite this