100 citations · 148 across the 10 of their papers we have counts for
10 papers
Partially dissipative systems in the critical regularity setting, and strong relaxation limit
Raphaël Danchin
Many physical phenomena may be modelled by first order hyperbolic equations with degenerate dissipative or diffusive terms. This is the case for example in gas dynamics, where the…
Partially dissipative one-dimensional hyperbolic systems in the critical regularity setting, and applications
Timothée Crin-Barat, Raphael Danchin
Here we develop a method for investigating global strong solutions of partially dissipative hyperbolic systems in the critical regularity setting. Compared to the recent works by K…
Free Boundary Problems via Da Prato-Grisvard Theory
Raphaël Danchin, Matthias Hieber, Piotr B. Mucha +1
An -maximal regularity theory for parabolic evolution equations inspired by the pioneering work of Da Prato and Grisvard is developed. Besides of its own interest, th…
On the persistence of Hölder regular patches of density for the inhomogeneous Navier-Stokes equations
Raphaël Danchin, Xin Zhang
In our recent work dedicated to the Boussinesq equations [Danchin and Zhang 2016], we established the persistence of solutions with piecewise constant temperature along interfaces…
A Frequency Space for the Heisenberg Group
Hajer Bahouri, Jean-Yves Chemin, Raphael Danchin
We here revisit Fourier analysis on the Heisenberg group H^d. Whereas, according to the standard definition, the Fourier transform of an integrable function f on H^d is a one param…
Diffusive limits for a barotropic model of radiative flow
Raphaël Danchin, Bernard Ducomet
Here we aim at justifying rigorously different types of physically relevant diffusive limits for radiative flows. For simplicity, we consider the barotropic situation, and adopt th…