Translator Disclaimer
March/April 2018 Horizontal Biot-Savart law in general dimension and an application to the 4D magneto-hydrodynamics
Kazuo Yamazaki
Differential Integral Equations 31(3/4): 301-328 (March/April 2018).

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.

Citation

Download Citation

Kazuo Yamazaki. "Horizontal Biot-Savart law in general dimension and an application to the 4D magneto-hydrodynamics." Differential Integral Equations 31 (3/4) 301 - 328, March/April 2018.

Information

Published: March/April 2018
First available in Project Euclid: 19 December 2017

zbMATH: 06837099
MathSciNet: MR3738200

Subjects:

Rights: Copyright © 2018 Khayyam Publishing, Inc.

JOURNAL ARTICLE
28 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.31 • No. 3/4 • March/April 2018
Back to Top