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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:
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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