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An Approach to Incompressible Models: Exploring the Case of Regular Solutions
- Speaker(s)
- Piotr B. Mucha
- Affiliation
- University of Warsaw
- Language of the talk
- English
- Date
- Dec. 19, 2024, 12:30 p.m.
- Room
- room 5070
- Seminar
- Seminar of Mathematical Physics Equations Group
This talk presents two distinct approaches to the approximation of incompressible flow models. Both strategies employ a penalization technique on $ν div u$ by allowing the viscous (bulk) viscosity coefficient to approach infinity, thereby facilitating the transition from compressible to incompressible flow dynamics. The first approach is derived from the compressible Navier-Stokes system. This method provides a framework for understanding incompressible solutions' properties and reveals interesting interactions and behaviors within compressible flows. Through this lens, we can gain valuable insights into the underlying mechanisms governing fluid behavior in various regimes. The second approach involves a limit analysis of the
parabolic system governed by the Lam ́e operator with a compressible coefficient as it tends to infinity. This method offers a different perspective, focusing on the stability and convergence of solutions within the context of parabolic systems.
While both approaches operate within the framework of regular solutions, the methodologies and interpretations differ significantly, leading to unique findings and implications for studying fluid dynamics. This talk will explore these differences in depth and discuss their relevance in both theoretical and applied contexts. The research presented is based on collaborative works with Rapha ̈el Danchin, Tomasz Piasecki, and Patrick Tolksdorf.
parabolic system governed by the Lam ́e operator with a compressible coefficient as it tends to infinity. This method offers a different perspective, focusing on the stability and convergence of solutions within the context of parabolic systems.
While both approaches operate within the framework of regular solutions, the methodologies and interpretations differ significantly, leading to unique findings and implications for studying fluid dynamics. This talk will explore these differences in depth and discuss their relevance in both theoretical and applied contexts. The research presented is based on collaborative works with Rapha ̈el Danchin, Tomasz Piasecki, and Patrick Tolksdorf.
