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Limiting case of the Sobolev inequality in BMO, with application to the Euler equations. (English) Zbl 0985.46015
The authors prove (Theorem 1) $\|f |L_\infty \|\leq c \left[ 1 + \|f |\text{BMO} \|\left( 1 + \log^+ \|f |W^s_p \|\right) \right],$ where $$1 < p < \infty$$ and $$s > \frac{n}{p}$$. Here $$W^s_p (R^n)$$ are the Sobolev spaces in $$\mathbb{R}^n$$. They apply this result to Euler equations for imcompressible fluid motions in $$\mathbb{R}^n$$ (Theorem 2).

##### MSC:
 4.6e+36 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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