摘要
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 Danchim Through our methods, we can get optimal time decay rate with initial data just small in B^N/2-1,N/2＋1∩^N/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 B^N/2-2,N/2 ∩B^N/2-1 to get the optimal time decay rate in space L2.
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 Danchim Through our methods, we can get optimal time decay rate with initial data just small in B^N/2-1,N/2＋1∩^N/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 B^N/2-2,N/2 ∩B^N/2-1 to get the optimal time decay rate in space L2.
基金
Supported by the National Natural Science Foundation of China(Grant No.11501439)
the Postdoctoral Science Foundation Pro ject of China(Grant No.2017T100733)
