Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • Global existence for the magnetohydrodynamic system in critical spaces

  • Hammadi Abidi, Marius Paicu
  • Journal:
    Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 138 / Issue 3 / June 2008
    Published online by Cambridge University Press:
    14 July 2008, pp. 447-476
    Print publication:
    June 2008

  • In this article, we show that the magnetohydrodynamic system in $\mathbb{R}^N$ with variable density, variable viscosity and variable conductivity has a local weak solution in the Besov space $\dot{B}^{N/p_1}_{p_1,1}(\mathbb{R}^N)\times\dot{B}^{(N/p_2)-1}_{p_2,1}(\mathbb{R}^N) \times\dot{B}^{(N/p_2)-1}_{p_2,1}(\mathbb{R}^N)$ for all $1<p_2<+\infty$ and some $1<p_1\leq2N/3$ if the initial density approaches a positive constant. Moreover, this solution is unique if we impose the restrictive condition $1<p_2\leq2N$. We also prove that the constructed solution exists globally in time if the initial data are small. In particular, this allows us to work in the framework of Besov space with negative regularity indices and this fact is particularly important when the initial data are strongly oscillating.