| Abstract: |
| In this talk we present several recent results on the mathematical analysis of Voigt-type regularizations of fluid flow models. These models extend the classical Navier-Stokes framework by incorporating relaxation or viscoelastic effects, leading to improved analytical properties while preserving the main features of the fluid dynamics models.
We study different formulations of these systems, including generalized power-law models, flows with non-homogeneous density, and models allowing the presence of vacuum regions.
For the associated nonlinear initial-boundary value problems, we establish results on the existence, uniqueness, and regularity of weak and strong solutions under suitable assumptions on the nonlinear exponents and the spatial dimension.
We also investigate qualitative properties of the solutions, including long-time behavior and decay rates in the presence of source or sink terms, as well as smoothing and decay mechanisms for the linearized barotropic Navier-Stokes-Voigt system.
These results contribute to a unified mathematical framework for the analysis of Voigt-regularized fluid models. |
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