Optimal Time Decay of Navier–Stokes Equations with Low Regularity Initial Data
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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 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  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.
KeywordsCompressible fluids besov space framework optimal time decay negative Besov space
MR(2010) Subject Classification76N10 35Q30 35Q35
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