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

Sazonov, L. I.

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 \(t\to\infty\).

MSC:

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

Keywords:

Oseen semigroup; perturbed nonlinear Oseen system; power \(L_p\)-\(L_q\) estimates; Navier-Stokes system; solenoidal field; Cauchy problem; Fourier transform

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