| Autor: |
Agélas, Léo |
| Zdroj: |
Monatshefte für Mathematik; Oct2016, Vol. 181 Issue 2, p245-266, 22p |
| Abstrakt: |
In this article, the two-dimensional magneto-hydrodynamic (MHD) equations are considered with only magnetic diffusion. Here the magnetic diffusion is given by $${\mathfrak D}$$ a Fourier multiplier whose symbol m is given by $$m(\xi )=|\xi |^2\log (e+|\xi |^2)^\beta $$ . We prove that there exists an unique global solution in $$H^s(\mathbb {R}^2)$$ with $$s>2$$ for these equations when $$\beta >1$$ . This result improves the previous works which require that $$m(\xi )=|\xi |^{2\beta }$$ with $$\beta >1$$ and brings us closer to the resolution of the well-known global regularity problem on the 2D MHD equations with standard Laplacian magnetic diffusion, namely $$m(\xi )=|\xi |^2$$ . [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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