3 papers
math.AP2026
Three-scale singular limits with applications to rapidly rotating fluids and the hyperbolization of dispersive systems
Vincent Duchêne, Arnaud Duran, Khawla Msheik
We consider singular problems for a general class of quasilinear hyperbolic systems that involve two a priori independent stiff parameters. We argue that such situations may lead t…
math.NA2025
The Fourier spectral approach to the spatial discretization of quasilinear hyperbolic systems
Vincent Duchêne, Johanna Ulvedal Marstrander
We discuss the rigorous justification of the spatial discretization by means of Fourier spectral methods of quasilinear first-order hyperbolic systems. We provide uniform stability…
math.AP2024
On the hydrostatic limit of stably stratified fluids with isopycnal diffusivity
Vincent Duchêne, Roberta Bianchini
This article is concerned with rigorously justifying the hydrostatic limit for continuously stratified incompressible fluids under the influence of gravity. The main distinction of…