THE GLOBAL EXISTENCE AND A DECAY ESTIMATE OF SOLUTIONS TO THE PHAN-THEIN-TANNER MODEL

doi:10.1007/s10473-022-0314-6

Abstract

Abstract: 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 $L^p-L^2(1\leq p\leq2)$ type of the decay rate without requiring that the $L^p$ norm of initial data is small.

Key words: Phan-Thein-Tanner model, global existence, time decay rates

CLC Number:

35Q30

Ruiying WEI, Yin LI, Zheng-an YAO. THE GLOBAL EXISTENCE AND A DECAY ESTIMATE OF SOLUTIONS TO THE PHAN-THEIN-TANNER MODEL[J].Acta mathematica scientia,Series A, 2022, 42(3): 1058-1080.

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