TIME GLOBAL MILD SOLUTIONS OF NAVIER-STOKES-OSEEN EQUATIONS

doi:10.1007/s10473-021-0209-y

Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (2): 450-460.doi: 10.1007/s10473-021-0209-y

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TIME GLOBAL MILD SOLUTIONS OF NAVIER-STOKES-OSEEN EQUATIONS

Viet Duoc TRINH^1,2

1. Faculty of Mathematics, Mechanics and Informatics, University of Science, Vietnam National University, Hanoi, 334 Nguyen Trai, Hanoi, Vietnam;
2. Thang Long Institute of Mathematics and Applied Sciences, Nghiem Xuan Yem, Hanoi, Vietnam

Received:2020-01-21 Revised:2020-04-21 Online:2021-04-25 Published:2021-04-29
About author:Viet Duoc TRINH,E-mail:tvduoc@gmail.com,duoctv@vnu.edu.vn
Supported by:
This research is funded by the Vietnam National University, Hanoi (VNU) under project number QG.17.07.

Abstract

Abstract: In this paper we prove the existence and uniqueness of time global mild solutions to the Navier-Stokes-Oseen equations, which describes dynamics of incompressible viscous fluid flows passing a translating and rotating obstacle, in the solenoidal Lorentz space $L_{\sigma, {\rm{w}}}^3$. Besides, boundedness and polynomial stability of these solutions are also shown.

Key words: Time global mild solutions, Navier-Stokes-Oseen equations, Oseen operator, rotating and translating obstacle

CLC Number:

35B35

Viet Duoc TRINH. TIME GLOBAL MILD SOLUTIONS OF NAVIER-STOKES-OSEEN EQUATIONS[J].Acta mathematica scientia,Series B, 2021, 41(2): 450-460.

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TIME GLOBAL MILD SOLUTIONS OF NAVIER-STOKES-OSEEN EQUATIONS

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