Related papers: Low-Mach-number Euler equations with solid-wall bo…
We consider the Cauchy problem for the full free boundary Euler equations in $3$d with an initial small velocity of size $O(\epsilon_0)$, in a moving domain which is initially an $O(\epsilon_0)$ perturbation of a flat interface. We assume…
The free-boundary compressible 1-D Euler equations with moving physical vacuum boundary are a system of hyperbolic conservation laws which are both characteristic and degenerate. The physical vacuum singularity (or rate-of-degeneracy)…
We design an energy-stable and asymptotic-preserving finite volume scheme for the compressible Euler system. Using the relative energy framework, we establish rigorous error estimates that yield convergence of the numerical solutions in two…
We investigate the pressureless fractional Euler-alignment system with nonlinear velocity couplings, referred to as the $p$-Euler-alignment system. This model features a nonlinear velocity alignment force, interpreted as a density-weighted…
We prove that the 3-D compressible Euler equations with surface tension along the moving free-boundary are well-posed. Specifically, we consider isentropic dynamics and consider an equation of state, modeling a liquid, given by Courant and…
The strong convergence of Euler approximations of stochastic delay differential equations is proved under general conditions. The assumptions on drift and diffusion coefficients have been relaxed to include polynomial growth and only…
We obtain a general sufficient condition on the geometry of possibly singular planar domains that guarantees global uniqueness for any weak solution to the Euler equations on them whose vorticity is bounded and initially constant near the…
We introduce a new wave formulation for the relativistic Euler equations with vacuum boundary conditions that consists of a system of non-linear wave equations in divergence form with a combination of acoustic and Dirichlet boundary…
We consider the $\alpha$-Euler equations on a bounded three-dimensional domain with frictionless Navier boundary conditions. Our main result is the existence of a strong solution on a positive time interval, uniform in $\alpha$, for…
We consider the low Mach number limit problem of the Euler equations for isentropic fluids in the analytic spaces. We prove that, given general analytic initial data, the solution is uniformly bounded on a time interval independent of the…
A class of three-dimensional initial data characterized by uniformly large vorticity is considered for the Euler equations of incompressible fluids. The fast singular oscillating limits of the Euler equations are studied for parametrically…
We consider the incompressible Euler equations in $R^2$ when the initial vorticity is bounded, radially symmetric and non-increasing in the radial direction. Such a radial distribution is stationary, and we show that the monotonicity…
We consider concentrated vorticities for the Euler equation on a smooth domain $\Omega \subset \mathbf{R}^2$ in the form of \[ \omega = \sum_{j=1}^N \omega_j \chi_{\Omega_j}, \quad |\Omega_j| = \pi r_j^2, \quad \int_{\Omega_j} \omega_j d\mu…
Global existence for the nonisentropic compressible Euler equations with vacuum boundary for all adiabatic constants $\gamma > 1$ is shown through perturbations around a rich class of background nonisentropic affine motions. The notable…
We study the long-time behavior of solutions to the compressible Euler equations with frictional damping in the whole space, where we prescribe direction-dependent values for the density at spatial infinity. To this end, we transform the…
An asymptotic preserving and energy stable scheme for the barotropic Euler system under the low Mach number scaling is designed and analysed. A velocity shift proportional to the pressure gradient is introduced in the convective fluxes,…
We prove well-posedness for the 3-D compressible Euler equations with moving physical vacuum boundary, with an equation of state given by the so-called gamma gas-law for gamma > 1. The physical vacuum singularity requires the sound speed c…
Global stability of the spherically symmetric nonisentropic compressible Euler equations with positive density around global-in-time background affine solutions is shown in the presence of free vacuum boundaries. Vacuum is achieved despite…
We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modelling a one-dimensional linearly elastic body interacting with a rigid substrate through an adhesive…
We study the Cauchy problem for the $3D$ compressible Euler equations under an arbitrary equation of state with positive speed of sound, aside from that of a Chaplygin gas. For open sets of smooth initial data with non-trivial vorticity and…