𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Well-posedness for the incompressible magneto-hydrodynamic system

✍ Scribed by Changxing Miao; Baoquan Yuan; Bo Zhang

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
158 KB
Volume
30
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

This paper is concerned with well‐posedness of the incompressible magneto‐hydrodynamics (MHD) system. In particular, we prove the existence of a global mild solution in BMO^−1^ for small data which is also unique in the space C([0, ∞); BMO^−1^). We also establish the existence of a local mild solution in bmo^−1^ for small data and its uniqueness in C([0, T); bmo^−1^). In establishing our results an important role is played by the continuity of the bilinear form which was proved previously by Kock and Tataru. In this paper, we give a new proof of this result by using the weighted L^p^‐boundedness of the maximal function. Copyright © 2006 John Wiley & Sons, Ltd.

📜 SIMILAR VOLUMES

Well-posedness of the Hydrodynamic Model
Well-posedness of the Hydrodynamic Model for Semiconductors
✍ Li-Ming Yeh 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 824 KB

## Communicated by B. Brosowski This paper concerns the well-posedness of the hydrodynamic model for semiconductor devices, a quasilinear elliptic-parbolic-hyperbolic system. Boundary conditions for elliptic and parabolic equations are Dirichlet conditions while boundary conditions for the hyperbo

On the well-posedness of the Cauchy prob
On the well-posedness of the Cauchy problem for an MHD system in Besov spaces
✍ Changxing Miao; Baoquan Yuan 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 206 KB 👁 1 views

## Abstract This paper is devoted to the study of the Cauchy problem of incompressible magneto‐hydrodynamics system in the framework of Besov spaces. In the case of spatial dimension __n__⩾3, we establish the global well‐posedness of the Cauchy problem of an incompressible magneto‐hydrodynamics sys

Well-posedness and asymptotic analysis f
Well-posedness and asymptotic analysis for a Penrose–Fife type phase field system
✍ Riccarda Rossi 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 275 KB

## Abstract In this paper, an asymptotic analysis of the (non‐conserved) Penrose–Fife phase field system for two vanishing time relaxation parameters ε and δ is developed, in analogy with the similar analyses for the phase field model proposed by G. Caginalp (__Arch. Rational Mech. Anal__. 1986; **