【摘要】：本文主要研究關(guān)于三維可壓縮Oldroyd-B模型的全局適定性問題及其強解的衰減率問題。Oldroyd-B模型是粘彈性流體中的一個經(jīng)典課題。關(guān)于可壓和不可壓Oldroyd-B模型的局部解、強解以及衰減問題近幾年都有不同角度的探討。其中,可壓縮Oldroyd-B模型,在給出初值為小量,并且偶合常數(shù)ω不為小量的條件下,已經(jīng)有局部解的存在性證明。本文中,我們在此前提下證得Oldroyd-B模型下的方程組在給出初值的條件下有唯一的全局強解,并在H2框架下接近恒定的平衡態(tài)。另外,如果初始值在L1上,那么解在Lp(≤ p ≤ 6)模下的收斂率及L2模下的空間倒數(shù)的收斂率都可以得到。
[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，

本文編號：2478244