Flow around an obstacle. Domain dependence
There are two applications of domain stability results for the governing equations of the in/out flow problem: The first is to the existence of weak renormalized solutions with reasonable regularity assumptions on the data from the point of view of applications. This means that at the first stage the existence is obtained under restrictive assumptions, in particular on the domain. Next, the assumptions are relaxed by applying the stability result. In this important direction we have a nice result: a closed obstacle is perfectly admissible for the existence of weak renormalized solutions for compressible Navier-Stokes equations. In other words, there is no need for artificial domain constraints—solutions for the governing equations exist even in the case of a closed obstacle.
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