Some interpolation inequalities involving Stokes operator and first order derivatives
The author proves various multiplicative inequalities of the type \[ \|w\|_r \leq c \|P\Delta w\|_p^a \|w\|_q^{1-a}, \tag{1} \] where \(0\leq a \leq 1\), \(P\Delta\) is the Stokes operator in an exterior domain \(\Omega\) in \({\mathbb{R}}^n , n\geq 2\), with sufficiently smooth boundary, and \(\|w\|_p \) is the \(L^p(\Omega)\)-norm. The function \(w\) is taken from appropriate spaces. Analogues of (1), where \(w\) in the left-hand side of (1) is replaced by \(\nabla w\), are also established.
scientific article; zbMATH DE number 1471595
scientific article