Olivier Lafitte

Stability of Isentropic Navier–Stokes Shocks in the High-Mach Number Limit

By a combination of asymptotic ODE estimates and numerical Evans function calculations, we establish stability of viscous shock solutions of the isentropic compressible Navier–Stokes equations with γ-law pressure (i) in the limit as Mach number M goes to infinity, for any γ ≥ 1 (proved analytically), and (ii) for M ≥ 2,500,

EXISTENCE AND STABILITY OF VISCOUS SHOCK PROFILES FOR 2-D ISENTROPIC MHD WITH INFINITE ELECTRICAL RESISTIVITY

{\gamma\in [1,2.5]}

The kernel of the neumann operator for a strictly diffractive analytic problem

or M ≥ 13,000,

Theoretical Study of an Abstract Bubble Vibration Model

{\gamma \in [2.5,3]}

Mechanical stress increases brain amyloid β, tau, and α-synuclein concentrations in wild-type mice

(demonstrated numerically). This builds on and completes earlier studies by Matsumura–Nishihara and Barker–Humpherys–Rudd–Zumbrun establishing stability for low and intermediate Mach numbers, respectively, indicating unconditional stability, independent of shock amplitude, of viscous shock waves for γ-law gas dynamics in the range