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math.AP2026
Well-posedness of a first-order formulation for fractionally damped nonlinear acoustics
Pascal Lehner, Mostafa Meliani
In this work, we study the well-posedness of a quasilinear first-order-in-time system with memory arising in nonlinear acoustics. The model features a memory kernel describing the…
math.AP2025
Blow-up criterion for the compressible Navier--Stokes system with inflow-outflow boundary conditions
Anna Abbatiello, Mostafa Meliani
We consider the compressible Navier-Stokes system in three dimensions with general inflow-outflow boundary conditions, meaning that we prescribe a boundary velocity which has non-z…
math.AP2025
existence for the open compressible MHD system
Mostafa Meliani
We study the local existence of solutions to the magnetohydrodynamics (MHD) system describing the motion of a compressible, viscous, electrically and heat conducting fluid in the $…