Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Regularity criteria of axisymmetric weak solutions to the 3D magnetohydrodynamic equations

Regularity criteria of axisymmetric weak solutions to the 3D magnetohydrodynamic equations In this paper, we study the regularity criteria for axisymmetric weak solutions to the MHD equations in ℝ3. Let ω θ , J θ and u θ be the azimuthal component of ω, J and u in the cylindrical coordinates, respectively. Then the axisymmetric weak solution (u, b) is regular on (0, T) if (ω θ , J θ ) ∈ L q (0, T; L p ) or (ω θ , ▽(u θ e θ )) ∈ L q (0, T; L p ) with $$\tfrac{3} {p} + \tfrac{2} {q} \leqslant 2, \tfrac{3} {2} < p < \infty$$ . In the endpoint case, one needs conditions $$\left( {\omega _\theta ,J_\theta } \right) \in L^1 \left( {0,T;\dot B_{\infty ,\infty }^0 } \right)$$ or $$\left( {\omega _\theta ,\nabla \left( {u_\theta e_\theta } \right)} \right) \in L^1 \left( {0,T;\dot B_{\infty ,\infty }^0 } \right)$$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Regularity criteria of axisymmetric weak solutions to the 3D magnetohydrodynamic equations

Loading next page...
 
/lp/springer-journals/regularity-criteria-of-axisymmetric-weak-solutions-to-the-3d-duls0vOUyS
Publisher
Springer Journals
Copyright
Copyright © 2013 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-013-0223-5
Publisher site
See Article on Publisher Site

Abstract

In this paper, we study the regularity criteria for axisymmetric weak solutions to the MHD equations in ℝ3. Let ω θ , J θ and u θ be the azimuthal component of ω, J and u in the cylindrical coordinates, respectively. Then the axisymmetric weak solution (u, b) is regular on (0, T) if (ω θ , J θ ) ∈ L q (0, T; L p ) or (ω θ , ▽(u θ e θ )) ∈ L q (0, T; L p ) with $$\tfrac{3} {p} + \tfrac{2} {q} \leqslant 2, \tfrac{3} {2} < p < \infty$$ . In the endpoint case, one needs conditions $$\left( {\omega _\theta ,J_\theta } \right) \in L^1 \left( {0,T;\dot B_{\infty ,\infty }^0 } \right)$$ or $$\left( {\omega _\theta ,\nabla \left( {u_\theta e_\theta } \right)} \right) \in L^1 \left( {0,T;\dot B_{\infty ,\infty }^0 } \right)$$ .

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Apr 10, 2013

References