𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Milton's conjecture on the regularity of solutions to isotropic equations

✍ Scribed by Daniel Faraco

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
179 KB
Volume
20
Category
Article
ISSN
0294-1449

No coin nor oath required. For personal study only.

✦ Synopsis

We present examples showing that the threshold for the integrability of the gradient of solutions to isotropic equations is 2K/(K -1). The main tools are p-laminates and Beltrami Operators.  2003 Éditions scientifiques et médicales Elsevier SAS MSC: 30C62; 49J45; 35J15 RÉSUMÉ. -Nous présentons des exemples, qui prouvent que le seuil de l'intégrabilité du gradient des solutions des équations isotropiques est 2K/(K -1). Les techniques principales sont les p-laminates et les opérateurs de Beltrami.

📜 SIMILAR VOLUMES

Remark on the regularity for weak soluti
Remark on the regularity for weak solutions to the magnetohydrodynamic equations
✍ Cheng He; Yun Wang 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 160 KB

## Abstract We study the regularity criteria for weak solutions to the incompressible magnetohydrodynamic (MHD) equations. Some regularity criteria, which are related only with __u__+__B__ or __u__−__B__, are obtained for weak solutions to the MHD equations. Copyright © 2008 John Wiley & Sons, Ltd.

A remark on the regularity of solutions
A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains
✍ Martin Costabel 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 202 KB

## Abstract Let u be a vector field on a bounded Lipschitz domain in ℝ^3^, and let u together with its divergence and curl be square integrable. If either the normal or the tangential component of u is square integrable over the boundary, then u belongs to the Sobolev space __H__^1/2^ on the domain

Extension criterion on regularity for we
Extension criterion on regularity for weak solutions to the 3D MHD equations
✍ Sadek Gala 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 138 KB 👁 1 views

In this paper, we consider the regularity criteria for weak solutions to the 3D incompressible magnetohydrodynamic equations and prove some regularity criteria which are related only with u+B or u-B. This is an improvement of the result given by He and Wang (J.