Hyperbolic approximations in fluid mechanics: Hypocoercivity and hybrid Besov spaces

Next Thursday November 23, 2023 our postdoctoral researcher Dr. Timothée Crin-Barat will talk on “Hyperbolic approximations in fluid mechanics: Hypocoercivity and hybrid Besov spaces” at the Nanjing University of Aeronautics and Astronautics.

Abstract. We investigate the relaxation limits associated with partially dissipative systems in the context of fluid mechanics. As we shall see, partially dissipative systems can be interpreted as hyperbolic approximations of parabolic systems and provide an element of response to the infinite speed of propagation paradox arising in viscous fluid mechan- ics. To demonstrate this, we study a hyperbolic approximation of the multi-dimensional compressible Navier-Stokes-Fourier system and establish its hyperbolic-parabolic strong relaxation limit. For this purpose, we use techniques from the hypocoercivity theory and a precise frequency decomposition of the solutions via the Littlewood-Paley theory. This is a joint work with S. Kawashima, J. Xu and E. Zuazua.

Then, we study the strong relaxation of the damped 2D-Boussinesq system to- ward the incompressible porous media equation. To that matter, we use an anisotropic Littlewood-Paley framework and develop new anisotropic product laws to lower the reg- ularity requirements on the initial data. This is a result (ARMA ’24) obtained in collab- oration with R. Bianchini and M. Paicu.
To conclude, we discuss possible extensions to these results and open problems.

Thu. November 23, 2023 at 10:00H (local time)

Nanjing University of Aeronautics and Astronautics
29 Yudao St., Nanjing, Jiangsu Province