论文标题
全球适应性，用于与应力扩散的粘弹性速率流体的二维流动
Global well-posedness for two-dimensional flows of viscoelastic rate-type fluids with stress diffusion
论文作者
论文摘要
我们考虑了与应力扩散的强大粘弹性速率型流体的二维流的部分微分方程系统，涉及一般的客观衍生物。研究的系统概括了不可压缩的navier-通过在本构方程中出现额外的术语的cauchy应力，该方程式是流体速度$ v $和压力$ p $的，该方程是根据正定张量$ b $表示的。张量$ b $根据方程式的扩散变体演变，该变体可以看作是Oldroyd-B和Giesekus模型的相应对应物的组合。考虑到空间周期性的问题，我们证明，对于任意的初始数据并强迫适当的$ l^2 $空间，存在着一个独特的全球定义的弱解决方案，对运动方程式有一个唯一的弱解决方案，并且更常规的初始数据并强迫使用$ \ bs b $正面确定的$ \ bs b $ pastic nater Pastic nathere。
We consider the system of partial differential equations governing two-dimensional flows of a robust class of viscoelastic rate-type fluids with stress diffusion, involving a general objective derivative. The studied system generalizes the incompressible Navier--Stokes equations for the fluid velocity $v$ and pressure $p$ by the presence of an additional term in the constitutive equation for the Cauchy stress expressed in terms of a positive definite tensor $B$. The tensor $B$ evolves according to a diffusive variant of an equation that can be viewed as a combination of corresponding counterparts of Oldroyd-B and Giesekus models. Considering spatially periodic problem, we prove that for arbitrary initial data and forcing in appropriate $L^2$ spaces, there exists a unique globally defined weak solution to the equations of motion, and more regular initial data and forcing launch a more regular solution with $\bs B$ positive definite everywhere.
