Related papers: On similarity flows for the compressible Euler sys…
A basic example of shear flow was introduced by DiPerna and Majda to study the weak limit of oscillatory solutions of the Euler equations of incompressible ideal fluids. In particular, they proved by means of this example that weak limit of…
In this article, we provide notes that complement the lectures on the relativistic Euler equations and shocks that were given by the second author at the program Mathematical Perspectives of Gravitation Beyond the Vacuum Regime, which was…
We prove weak-strong uniqueness in the class of admissible measure-valued solutions for the isentropic Euler equations in any space dimension and for the Savage-Hutter model of granular flows in one and two space dimensions. For the latter…
Using a very high precision spectral calculation applied to the incompressible and inviscid flow with initial condition $\psi_0(x_1, x_2) = \cos x_1+\cos 2x_2$, we find that the width $\delta(t)$ of its analyticity strip follows a…
We study singular limit for scaled barotropic Euler system modelling a rotating, compressible and inviscid fluid, where Mach and Rossby numbers are proportional to a small parameter $\epsilon$. If the fluid is confined to an infinite slab,…
In this article, we study the homogenization limit of a family of solutions to the incompressible 2D Euler equations in the exterior of a family of $n_k$ disjoint disks with centers $\{z^k_i\}$ and radii $\varepsilon_k$. We assume that the…
In this paper, we study the limiting behavior of Riemann solutions to the Euler equations of one-dimensional compressible fluid flow as $\gamma$ tends to one. We show that the limit solution forms the delta wave to the pressureless Euler…
We address the existence and stability of transonic shocks for the two-dimensional steady rotating Euler system in an almost flat nozzle. Under the influence of the Coriolis force, we first establish a class of special transonic shock…
Non-stationary Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some exact solutions by means of such a representation.…
We present our recent results on the Prandtl-Meyer reflection for supersonic potential flow past a solid ramp. When a steady supersonic flow passes a solid ramp, there are two possible configurations: the weak shock solution and the strong…
In this article we consider the inhomogeneous incompressible Euler equations describing two fluids with different constant densities under the influence of gravity as a differential inclusion. By considering the relaxation of the…
This paper is concerned with the inhomogeneous incompressible Euler system. We establish a Duchon--Robert type approximation theorem for the distribution describing the local energy flux of bounded solutions. The velocity field is assumed…
In this paper, we investigate steady inviscid compressible flows with radial symmetry in an annulus. The major concerns are transonic flows with or without shocks. One of the main motivations is to elucidate the role played by the angular…
The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of…
This note is devoted to the linear stability of the Couette flow for the non-isentropic compressible Euler equations in a domain $\mathbb{T}\times \mathbb{R}$. Exploiting the several conservation laws originated from the special structure…
Point vortex models are presented for the generalized Euler equations, which are characterized by a fractional Laplacian relation between the active scalar and the streamfunction. Special focus is given to the case of the surface…
In this paper, we study the two-dimensional steady compactly supported incompressible Euler equations with free boundaries. We consider flows with constant vorticity that are perturbations of annular equilibria, in contrast to the laminar…
In this paper a fully Eulerian solver for the study of multiphase flows for simulating the propagation of surface gravity waves over submerged bodies is presented. We solve the incompressible Navier-Stokes equations coupled with the volume…
Rotationally symmetric bodies with longitudinal cross sections of parabolic shape are frequently used to model astrophysical objects, such as magnetospheres and other blunt objects, immersed in interplanetary or interstellar gas or plasma…
We prove the existence of a subsonic axisymmetric weak solution $({\bf u},\rho,p)$ with ${\bf u}=u_x{\bf e}_x+u_r{\bf e}_r+u_\theta{\bf e}_{\theta}$ to steady Euler system in a three-dimensional infinitely long cylinder $\mathcal{N}$ when…