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Matematicheskie Zametki, 2012, Volume 91, Issue 6, Pages 880–895
DOI: https://doi.org/10.4213/mzm8888 (Mi mzm8888) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Estimates of Perturbed Oseen Semigroups and Their Applications to the Navier–Stokes System in $\mathbb{R}^n$

L. I. Sazonovab

a Southern Federal University, Rostov-on-Don
b South Mathematical Institute of VSC RAS
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DOI: https://doi.org/10.4213/mzm8888
Abstract: 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 $t\to \infty$.
Keywords: Oseen semigroup, perturbed nonlinear Oseen system, power $L_p-L_q$ estimates, Navier–Stokes system, solenoidal field, Cauchy problem, Fourier transform.
Received: 28.03.2010
Revised: 18.03.2011
English version:
Mathematical Notes, 2012, Volume 91, Issue 6, Pages 833–846
DOI: https://doi.org/10.1134/S0001434612050306
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: L. I. Sazonov, “Estimates of Perturbed Oseen Semigroups and Their Applications to the Navier–Stokes System in $\mathbb{R}^n$”, Mat. Zametki, 91:6 (2012), 880–895; Math. Notes, 91:6 (2012), 833–846
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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