一类粘弹性流体及其相关模型的若干数学问题研究

本项目研究一类粘弹性流体及其相关模型的适定性。Oldroyd-B模型是粘弹性流体的典型代表。 之前对Oldroyd-B模型的研究大多是在小初值整体解的框架下，本项目尝试给出某种大初值的结果。另外，之前的许多研究是针对耦合参数介于0和1之间粘性非退化的情形。在本项目，我们将研究耦合参数为1这种无粘情形。除此之外，当Weissenberg数趋于无穷时，我们还将考察低频时波算子的色散效应对粘弹性流体适定性的影响。我们的研究既涉及不可压缩流体，又涉及可压缩流体。

In this project, we will focus on the well-posedness issue of a class of viscoelastic fluids and related models. The Oldroyd-B model is a typical type of viscoelastic fluids. Most of the previous studies on the Oldroyd-B model are in the framework of small data. In this project, we will try to give some results with some kinds of large data. Moreover, for the Oldroyd-B model, we will also consider the inviscid case, i.e., the conpling constant equals 1. Besides, when the Weissenberg number tends to infinity, we will investigate the Cauchy problem of the viscoelastic fluids by virtue of the dispersive effect of the wave operator in the low frequency regime. Our research focus on incompressible and compressible fluids.