TY - JOUR
T1 - Stability of stationary solutions to the Navier–Stokes equations in the Besov space
AU - Kozono, Hideo
AU - Shimizu, Senjo
N1 - Funding Information:
The authors would like to express their sincere thanks to the referees for their valuable comments. The research of H. Kozono was partially supported by JSPS Grant‐in‐Aid for Scientific Research (S) 16H06339. The research of S. Shimizu was partially supported by JSPS Grant‐in‐Aid for Scientific Research (B) 16H03945.
Publisher Copyright:
© 2023 Wiley-VCH GmbH.
PY - 2023/5
Y1 - 2023/5
N2 - We consider the stability of the stationary solution w of the Navier–Stokes equations in the whole space (Formula presented.) for (Formula presented.). It is clarified that if w is small in (Formula presented.) for (Formula presented.) and (Formula presented.), then for every small initial disturbance (Formula presented.) with (Formula presented.) and (Formula presented.) ((Formula presented.)), there exists a unique solution (Formula presented.) of the nonstationary Navier–Stokes equations on (0, ∞) with (Formula presented.) such that (Formula presented.) and (Formula presented.) as (Formula presented.), for (Formula presented.), (Formula presented.), and small (Formula presented.).
AB - We consider the stability of the stationary solution w of the Navier–Stokes equations in the whole space (Formula presented.) for (Formula presented.). It is clarified that if w is small in (Formula presented.) for (Formula presented.) and (Formula presented.), then for every small initial disturbance (Formula presented.) with (Formula presented.) and (Formula presented.) ((Formula presented.)), there exists a unique solution (Formula presented.) of the nonstationary Navier–Stokes equations on (0, ∞) with (Formula presented.) such that (Formula presented.) and (Formula presented.) as (Formula presented.), for (Formula presented.), (Formula presented.), and small (Formula presented.).
KW - Navier–Stokes equations
KW - homogeneous Besov space
KW - stability
KW - stationary solution
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U2 - 10.1002/mana.202100150
DO - 10.1002/mana.202100150
M3 - Article
AN - SCOPUS:85147513556
SN - 0025-584X
VL - 296
SP - 1964
EP - 1982
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
IS - 5
ER -