Delta-type solutions for a system of induction equations with discontinuous velocity field
type: Item
instance of: scholarly article
zbMATH Open document ID: 1313.35335
author: A. I. Esina
author: A. I. Shafarevich
publication date: 2014-08-21T00:00:00Z
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 6333569
zbMATH Keywords: induction equations
zbMATH Keywords: delta-type solution
zbMATH Keywords: Green matrix
MaRDI profile type: Publication
title: Delta-type solutions for a system of induction equations with discontinuous velocity field
published in: Methods of Functional Analysis and Topology
review text: The authors study the Cauchy problem for the equation NEWLINE\[NEWLINE \frac{\partial B}{\partial t}+(V,\nabla )B-(B,\nabla )V=\varepsilon^2\mu \Delta B,\quad (\nabla,V)=(\nabla,B)=0,\quad t>0,x\in \mathbb R^n NEWLINE\]NEWLINE (\(n=2\, \text{or}\, 3\)). Here, \(B\) is a magnetic field, \(V\) is a given vector field (fluid velocity), and \(\varepsilon \to 0\). It is assumed that \(V\) changes rapidly in the vicinity of a surface. It is proved that the weak limit of the solution has a delta-type singularity on the surface. The Green matrix estimates and asymptotic series for solutions are obtained.
reviewed by: Anatoly N. Kochubei
description: scientific article; zbMATH DE number 6333569