16 papers
A lecture on Navier-Stokes equations
Sylvie Monniaux
The content of the following pages was part of a special topics lecture given at the Australian National University during the first semester of 2026. That was a very nice experice…
The Hall problem in domains
Sylvie Monniaux
In this paper, we develop a framework based on differential forms that enables us to deal with the Hall problem on domains in any dimension . In the case of smooth bounded d…
The magnetohydrodynamical system in bounded non smooth domains of dimension
Sylvie Monniaux
Existence of mild solutions for the magnetohydrodynamical system in C 1 domains is established in critical spaces in dimension n 3. The proof relies on recent regularity resul…
Strong solutions to the Keller-Segel-Navier-Stokes system in bounded Lipschitz domains
Matthias Hieber, Hideo Kozono, Sylvie Monniaux +1
Consider the coupled Keller-Segel-Navier-Stokes or the chemotaxis-consumption-Navier-Stokes system in bounded Lipschitz domains for general coupling terms which, e.g., include buoy…
Maximal regularity as a tool for partial differential equations
Sylvie Monniaux
In the last decades, a lot of progress has been made on the subject of maximal regularity. The property of maximal regularity is an a priori estimate and reads as follows: Fo…
Existence in critical spaces for the magnetohydrodynamical system in 3D bounded Lipschitz domains
Sylvie Monniaux
Existence of mild solutions for the 3D MHD system in bounded Lipschitz domains is established in critical spaces with the absolute boundary conditions.