Estimates of perturbed Oseen semigroups and their applications to the Navier-Stokes system in \(\mathbb R^n\). (English. Russian original) Zbl 1283.35067

Math. Notes 91, No. 6, 833-846 (2012); translation from Math. Zametki 91, No. 6, 880-895 (2012).
Summary: For perturbed Oseen semigroups in \(\mathbb R^n\), we establish their power \(L_p-L_q\) estimates. These estimates are used to prove the existence of small global solutions to perturbed nonlinear Oseen systems and also of estimates of their \(L_p\)-norms as \(t\to\infty\).


35Q30 Navier-Stokes equations
76D07 Stokes and related (Oseen, etc.) flows
76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text: DOI


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