In this paper,we study the global existence and decay rates of strong solutions to the three dimensional compressible Phan-Thein-Tanner model.By a refined energy method,we prove the global existence under the assumpti...In this paper,we study the global existence and decay rates of strong solutions to the three dimensional compressible Phan-Thein-Tanner model.By a refined energy method,we prove the global existence under the assumption that the H^(3) norm of the initial data is small,but that the higher order derivatives can be large.If the initial data belong to homogeneous Sobolev spaces or homogeneous Besov spaces,we obtain the time decay rates of the solution and its higher order spatial derivatives.Moreover,we also obtain the usual L^(p)-L^(2)(1≤p≤2)type of the decay rate without requiring that the Lpnorm of initial data is small.展开更多
基金partially supported by the National Natural Science Foundation of China(11926354,11971496)Natural Science Foundation of Guangdong Province(2019A1515011320,2021A1515010292,2214050001249)+2 种基金Innovative team project of ordinary universities of Guangdong Province(2020KCXTD024)Characteristic innovation projects of ordinary colleges and universities in Guangdong Province(2020KTSCX134)the Education Research Platform Project of Guangdong Province(2018179)。
文摘In this paper,we study the global existence and decay rates of strong solutions to the three dimensional compressible Phan-Thein-Tanner model.By a refined energy method,we prove the global existence under the assumption that the H^(3) norm of the initial data is small,but that the higher order derivatives can be large.If the initial data belong to homogeneous Sobolev spaces or homogeneous Besov spaces,we obtain the time decay rates of the solution and its higher order spatial derivatives.Moreover,we also obtain the usual L^(p)-L^(2)(1≤p≤2)type of the decay rate without requiring that the Lpnorm of initial data is small.
