Acta Mathematica Sinica, English Series

, Volume 34, Issue 5, pp 855–872 | Cite as

Optimal Time Decay of Navier–Stokes Equations with Low Regularity Initial Data

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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 H[N/2]+2(ℝ N ). 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 N/2−1,N/2+1N/2−1,N/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 N/2−2,N/2N/2−1 to get the optimal time decay rate in space L2.

Keywords

Compressible fluids besov space framework optimal time decay negative Besov space 

MR(2010) Subject Classification

76N10 35Q30 35Q35 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of MathematicsXi’an Jiaotong UniversityXi’anP. R. China
  2. 2.Beijing Center for Mathematics and Information Interdisciplinary Sciences (BCMIIS)BeijingP. R. China

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