## Abstract We prove local‐in‐time unique existence and a blowup criterion for solutions in the Triebel‐Lizorkin space for the Euler equations of inviscid incompressible fluid flows in ℝ^__n__^, __n__ ≥ 2. As a corollary we obtain global persistence of the initial regularity characterized by the Tr
✦ LIBER ✦
On the Well-posedness of the Ideal MHD Equations in the Triebel–Lizorkin Spaces
✍ Scribed by Qionglei Chen; Changxing Miao; Zhifei Zhang
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 220 KB
- Volume
- 195
- Category
- Article
- ISSN
- 0003-9527
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## Abstract We shall show that every strong solution __u__(__t__) of the Navier‐Stokes equations on (0, __T__) can be continued beyond __t__ > __T__ provided __u__ ∈ $L^{{{2} \over {1 - \alpha}}}$ (0, __T__; $\dot F^{- \alpha}\_{\infty ,\infty}$ for 0 < α < 1, where $\dot F^{s}\_{p,q}$ denotes the