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- Title
Optimal Time Decay of Navier-Stokes Equations with Low Regularity Initial Data.
- Authors
Jia, Jun Xiong
- Abstract
In this paper, we study the optimal time decay rate of isentropic Navier-Stokes equations under the low regularity assumptions about initial data. In the previous works about optimal time decay rate, the initial data need to be small in <italic>H</italic>[<italic>N</italic>/2]+2(ℝ<italic>N</italic>). Our work combined negative Besov space estimates and the conventional energy estimates in Besov space framework which is developed by Danchin. Through our methods, we can get optimal time decay rate with initial data just small in <italic>B̃</italic><italic>N</italic>/2−1,<italic>N</italic>/2+1 ∩ <italic>B̃</italic><italic>N</italic>/2−1,<italic>N</italic>/2 and belong to some negative Besov space (need not to be small). Finally, combining the recent results in [25] with our methods, we only need the initial data to be small in homogeneous Besov space <italic>B̃</italic><italic>N</italic>/2−2,<italic>N</italic>/2 ∩ <italic>B̃</italic><italic>N</italic>/2−1 to get the optimal time decay rate in space <italic>L</italic>2.
- Subjects
NAVIER-Stokes equations; BESOV spaces; FLUIDS; SOBOLEV spaces; GREEN'S functions
- Publication
Acta Mathematica Sinica, 2018, Vol 34, Issue 5, p855
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-017-6274-4