On Dissipative Solutions to a System Arising in Viscoelasticity
On Dissipative Solutions to a System Arising in Viscoelasticity
复制标题
粘弹性系统的耗散解
DOI：
10.1007/s00021-019-0459-9
复制
发表时间：
2019
影响因子：
1.3
通讯作者：
Martin Kalousek
中科院分区：
文献类型：
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作者：
Martin Kalousek
我们考虑一个不可压缩的粘弹性流体模型。它包括Navier-Stokes方程，包括应力张量中的弹性项和变形梯度演化的输运方程。本文的新特点是引入了耗散解的概念及其分析。我们表明，耗散的解决方案存在于全球任意有限能量的初始数据的时间和耗散的解决方案和强的解决方案，从相同的初始数据一致，只要后者存在。
We consider a model for an incompressible visoelastic fluid. It consists of the Navier–Stokes equations involving an elastic term in the stress tensor and a transport equation for the evolution of the deformation gradient. The novel feature of the paper is the introduction of the notion of a dissipative solution and its analysis. We show that dissipative solutions exist globally in time for arbitrary finite energy initial data and that a dissipative solution and a strong solution emanating from the same initial data coincide as long as the latter exists.