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Generalized solutions to models of compressible viscous fluids
Discrete and Continuous Dynamical Systems ( IF 1.1 ) Pub Date : 2020-10-14 , DOI: 10.3934/dcds.2020345
Anna Abbatiello , , Eduard Feireisl , Antoní Novotný , ,

We propose a new approach to models of general compressible viscous fluids based on the concept of dissipative solutions. These are weak solutions satisfying the underlying equations modulo a defect measure. A dissipative solution coincides with the strong solution as long as the latter exists (weak–strong uniqueness) and they solve the problem in the classical sense as soon as they are smooth (compatibility). We consider general models of compressible viscous fluids with non–linear viscosity tensor and non–homogeneous boundary conditions, for which the problem of existence of global–in–time weak/strong solutions is largely open.

中文翻译:

可压缩粘性流体模型的广义解

我们基于耗散解决方案的概念提出了一种新的通用可压缩粘性流体模型的方法。这些是满足缺陷测度模的基本方程的弱解。只要强解决方案存在,耗散解决方案就会与强解决方案相吻合(弱强唯一性),并且只要它们平滑(兼容),它们就可以解决经典意义上的问题。我们考虑具有非线性黏度张量和非均匀边界条件的可压缩粘性流体的一般模型,对于这些模型,全局及时弱/强解的存在存在很大问题。
更新日期:2020-11-16
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