Hypocoercivity in Algebraically Constrained Partial Differential Equations with Application to Oseen Equations

Authors

Franz Achleitner, Anton Arnold, Volker Mehrmann

Abstract

The long-time behavior of solutions to different versions of Oseen equations of fluid flow on the 2D torus is analyzed using the concept of hypocoercivity. The considered models are isotropic Oseen equations where the viscosity acts uniformly in all directions and anisotropic Oseen-type equations with different viscosity directions. The hypocoercivity index is determined (if it exists) and it is shown that similar to the finite dimensional case of ordinary differential equations and differential-algebraic equations it characterizes its decay behavior.

Keywords

Hypocoercivity (index); Dissipative systems; Constrained PDEs; Oseen equation; Primary 34A30; Secondary 34C11; 47F06; 35E05

Citation

• Journal: Journal of Dynamics and Differential Equations
• Year: 2023
• Volume:
• Issue:
• Pages:
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s10884-023-10327-6

BibTeX

@article{Achleitner_2023,
  title={{Hypocoercivity in Algebraically Constrained Partial Differential Equations with Application to Oseen Equations}},
  ISSN={1572-9222},
  DOI={10.1007/s10884-023-10327-6},
  journal={Journal of Dynamics and Differential Equations},
  publisher={Springer Science and Business Media LLC},
  author={Achleitner, Franz and Arnold, Anton and Mehrmann, Volker},
  year={2023}
}

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