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Zbl 0985.46015
Kozono, Hideo; Taniuchi, Yasushi
Limiting case of the Sobolev inequality in BMO, with application to the Euler equations.
(English)
[J] Commun. Math. Phys. 214, No.1, 191-200 (2000). ISSN 0010-3616; ISSN 1432-0916/e

The authors prove (Theorem 1) $$\|f |L_\infty \|\le c \left[ 1 + \|f |\text{BMO} \|\left( 1 + \log^+ \|f |W^s_p \|\right) \right],$$ where $1 < p < \infty$ and $s > \frac{n}{p}$. Here $W^s_p (R^n)$ are the Sobolev spaces in $\bbfR^n$. They apply this result to Euler equations for imcompressible fluid motions in $\bbfR^n$ (Theorem 2).
[Hans Triebel (Jena)]
MSC 2000:
*46E35 Sobolev spaces and generalizations

Keywords: BMO; limiting inequalities; Euler equation; imcompressible fluid motions

Cited in: Zbl 1180.46024

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