Speaker: Konstantina Trivisa (University of Maryland)
Title: Statistically stationary solutions to the stochastic isentropic compressible Euler equations with linear damping
Abstract: We investigate the long time behavior of isentropic compressible Euler equations with linear damping driven by a white-in-time noise, on a one-dimensional torus. We establish the existence of a statistically stationary solution--i.e., a solution whose law is invariant under the stochastic dynamics of the PDE--in the class of weak martingale entropy solutions for any adiabatic constant γ > 1 and any damping coefficient α > 0, which satisfies an associated entropy inequality. To establish this result, we use a multi-level approximation scheme consisting of a truncation parameter R and an artificial viscosity parameter ε.
Reference: J. Kuan, K. Tawri and K. Trivisa, Statistically stationary solutions to the stochastic isentropic compressible Euler equations with linear damping. Under revision JMPA (2026).