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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(ℝN). 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 B̃N/2−1,N/2+1 ∩ B̃N/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 B̃N/2−2,N/2 ∩ B̃N/2−1 to get the optimal time decay rate in space L2.

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Authors and Affiliations

  1. Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049, P. R. China

    Jun Xiong Jia

  2. Beijing Center for Mathematics and Information Interdisciplinary Sciences (BCMIIS), Beijing, 100190, P. R. China

    Jun Xiong Jia

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  1. Jun Xiong Jia
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Correspondence to Jun Xiong Jia.

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Supported by the National Natural Science Foundation of China (Grant No. 11501439) and the Postdoctoral Science Foundation Project of China (Grant No. 2017T100733)

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Jia, J.X. Optimal Time Decay of Navier–Stokes Equations with Low Regularity Initial Data. Acta. Math. Sin.-English Ser. 34, 855–872 (2018). https://doi.org/10.1007/s10114-017-6274-4

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  • DOI: https://doi.org/10.1007/s10114-017-6274-4

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