Existence theorem and blow-up criterion of strong solutions to the two-fluid MHD equation in ${\mathbb R}^3$
| dc.creator | Chen, Qionglei | |
| dc.creator | Miao, Changxing | |
| dc.date | 2006-11-07 | |
| dc.date | 2007-03-13 | |
| dc.date.accessioned | 2026-07-07T10:08:36Z | |
| dc.date.available | 2026-07-07T10:08:36Z | |
| dc.description | We first give the local well-posedness of strong solutions to the Cauchy problem of the 3D two-fluid MHD equations, then study the blow-up criterion of the strong solutions. By means of the Fourier frequency localization and Bony's paraproduct decomposition, it is proved that strong solution $(u,b)$ can be extended after $t=T$ if either $u\in L^q_T(\dot B^{0}_{p,\infty})$ with $\frac{2}{q}+\frac{3}{p}\le 1$ and $b\in L^1_T(\dot B^{0}_{\infty,\infty})$, or $(ω, J)\in L^q_T(\dot B^{0}_{p,\infty})$ with $\frac{2}{q}+\frac{3}{p}\le 2$, where $ω(t)=\na\times u $ denotes the vorticity of the velocity and $J=\na\times b$ the current density. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611165 | |
| dc.identifier | http://arxiv.org/abs/math/0611165 | |
| dc.identifier | J. Differential Equations 239 (2007)251-271 | |
| dc.identifier | doi:10.1016/j.jde.2007.03.029 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171049 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35B65; 76W05 | |
| dc.title | Existence theorem and blow-up criterion of strong solutions to the two-fluid MHD equation in ${\mathbb R}^3$ | |
| dc.type | text |