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The large time behavior of solutions to 3D Navier–Stokes equations with nonlinear damping
Author(s) -
Jiang Zaihong,
Zhu Mingxuan
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1540
Subject(s) - mathematics , nonlinear system , navier–stokes equations , norm (philosophy) , mathematical analysis , initial value problem , cauchy problem , term (time) , physics , compressibility , mechanics , law , quantum mechanics , political science
This paper studies the Cauchy problem of the 3D Navier–Stokes equations with nonlinear damping term | u | β −1 u ( β ≥ 1). For β ≥ 3, we derive a decay rate of the L 2 ‐norm of the solutions. Then, the large time behavior is given by comparing the equation with the classic 3D Navier–Stokes equations. Copyright © 2011 John Wiley & Sons, Ltd.