三维可压缩oldroyd-B模型的全局适定性和衰减率

发布时间：2019-05-16 11:13

【摘要】：本文主要研究关于三维可压缩Oldroyd-B模型的全局适定性问题及其强解的衰减率问题。Oldroyd-B模型是粘弹性流体中的一个经典课题。关于可压和不可压Oldroyd-B模型的局部解、强解以及衰减问题近几年都有不同角度的探讨。其中,可压缩Oldroyd-B模型,在给出初值为小量,并且偶合常数ω不为小量的条件下,已经有局部解的存在性证明。本文中,我们在此前提下证得Oldroyd-B模型下的方程组在给出初值的条件下有唯一的全局强解,并在H2框架下接近恒定的平衡态。另外,如果初始值在L1上,那么解在Lp(≤ p ≤ 6)模下的收敛率及L2模下的空间倒数的收敛率都可以得到。
[Abstract]:In this paper, we mainly study the global well-posedness problem of three-dimensional compressible Oldroyd-B model and the attenuation rate of its strong solution. Oldroyd-B model is a classical subject in Viscoelastic fluid. In recent years, the local solutions, strong solutions and attenuation problems of compressible and incompressible Oldroyd-B models have been discussed from different angles. Among them, the squeezed Oldroyd-B model has been proved to have the existence of local solutions under the condition that the initial value is small and the coupling constant 蠅 is not small. In this paper, we prove that the equations under the Oldroyd-B model have unique global strong solutions under the condition that the initial values are given, and are close to the constant equilibrium state in the H _ 2 framework. In addition, if the initial value is on L 1, then the convergence rate of the solution under Lp (鈮，

本文编号：2478244