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Large time behavior of isentropic compressible Navier–Stokes system in ℝ3

✍ Scribed by Hai-Liang Li; Ting Zhang

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
211 KB
Volume
34
Category
Article
ISSN
0170-4214

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✦ Synopsis

We consider the long-time behavior and optimal decay rates of global strong solution to three-dimensional isentropic compressible Navier-Stokes (CNS) system in the present paper. When the regular initial data also belong to some Sobolev space H l (R 3 )∩ Ḃ-s 1,∞ (R 3 ) with l 4 and s ∈ [0, 1], we show that the global solution to the CNS system converges to the equilibrium state at a faster decay rate in time. In particular, the density and momentum converge to the equilibrium state at the rates (1+t) -3/4-s/2 in the L 2 -norm or (1+t) -3/2-s/2 in the L ∞ -norm, respectively, which are shown to be optimal for the CNS system.

📜 SIMILAR VOLUMES

The large time behavior of solutions to
The large time behavior of solutions to 3D Navier–Stokes equations with nonlinear damping
✍ Zaihong Jiang; Mingxuan Zhu 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 111 KB 👁 1 views

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