Uniqueness and energy balance for isentropic Euler equation with stochastic forcing

Isentropic Euler equation

An all speed scheme for the Isentropic Euler equation is presented in this paper. When the Mach number tends to zero, the compressible Euler equation converges to its incompressible counterpart, in which the density becomes a constant. Increasing approximation errors and severe stability constraints are the main difficulty in the low Mach regime. The key idea of our all speed scheme is the spec...

A controllability result for the 1-D isentropic Euler equation

In the above equation, t is the time x is the position, ρ = ρ(t, x) ≥ 0 is the density of the fluid, m(t, x) is the momentum (v(t, x) = m(t,x) ρ(t,x) is the velocity of the fluid), the pressure law is p(ρ) = κρ γ , γ ∈ (1, 3]. Equation (EI) is formulated in Eulerian coordinates. The problem of one-dimensional isentropic gas dynamics is also frequently studied in Lagrangian coordinates: { ∂tτ − ...

Invariant measures for Burgers equation with stochastic forcing

On Isentropic Approximations for Compressible Euler Equations

In this paper, we first generalize the classical results on Cauchy problem for positive symmetric quasilinear systems to more general Besov space. Through this generalization, we obtain the local well-posedness with initial data in the space B d 2 +1 2,1 (R ) which has critical regularity index. We then apply these results to give an explicit characterization on the Isentropic approximation for...

Variational Particle Schemes for the Porous Medium Equation and for the System of Isentropic Euler Equations

Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these variational characterizations instead of the partial differential equations themselves, we obtain new schemes with remarkable stability properties. We show that they c...