Related papers: Incompressible and fast rotation limits for 3D com…
The work addresses a singular limit for a rotating compressible Euler system in the low Mach number and low Rossby number regime. Based on the concept of dissipative measure-valued solution, the quasi-geostrophic system is identified as the…
In this paper, we consider the low Mach and Rossby number singular limits and longtime existence of strong solution to the initial value problem of 3D compressible rotating Euler equations with ill-prepared initial data. We establish the…
This paper is devoted to the study of the low Mach number limit for the 2D isentropic Euler system associated to ill-prepared initial data with slow blow up rate on $\log\varepsilon^{-1}$. We prove in particular the strong convergence to…
In the present paper, we study the fast rotation limit for the density-dependent incompressible Euler equations in two space dimensions with the presence of the Coriolis force. In the case when the initial densities are small perturbation…
The low Mach number limit for the full compressible magnetohydrodynamic equations with general initial data is rigorously justified in the whole space $\mathbb{R}^3$. The uniform in Mach number estimates of the solutions in a Sobolev space…
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 the present thesis, we are interested in the description of the dynamics of flows on large scales. In this context, the fluids are governed by rotational, weak compressibility and stratification effects, whose importance is measured by…
In this article our goal is to study the singular limits for a scaled barotropic Euler system modelling a rotating, compressible and inviscid fluid, where Mach number $=\epsilon^m $, Rossby number $=\epsilon $ and Froude number $=\epsilon^n…
We study the singular limit of a rotating compressible fluid described by a scaled barotropic Navier-Stokes system, where the Rossby number, the Mach number and the Froude number tend to 0 in a particular mutual rate while the Reynolds…
We study in this paper the low Mach number limit for the 2d isentropic Euler system with ill-prepared initial data belonging to the critical Besov space $B_{2,1}^2$. By combining Strichartz estimates with the special structure of the…
We consider the compressible Euler equation with a Coriolis term and prove a lower bound on the time of existence of solutions in terms of the speed of rotation, sound speed and size of the initial data. Along the way, we obtain precise…
We consider a singular limit problem for the Navier-Stokes system of a rotating compressible fluid, where the Rossby and Mach numbers tend simultaneously to zero. The limit problem is identified as the 2-D Navier-Stokes system in the…
We study a singular limit for the compressible Navier-Stokes system when the Mach and Rossby numbers are proportional to certain powers of a small parameter $\ep$. If the Rossby number dominates the Mach number, the limit problem is…
The motion of a compressible inviscid radiative flow can be described by the radiative Euler equations, which consists of the Euler system coupled with a Poisson equation for the radiative heat flux through the energy equation. Although…
We study the incompressible limit of the compressible non-isentropic magnetohydrodynamic equations with zero magnetic diffusivity and general initial data in the whole space $\mathbb{R}^d$ $(d=2,3)$. We first establish the existence of…
In this paper, we consider the steady irrotational Euler flows in multidimensional nozzles. The first rigorous proof on the existence and uniqueness of the incompressible flow is provided. Then, we justify the corresponding low Mach number…
In this article, we verify the low Mach number limit of strong solutions to the non-isentropic compressible magnetohydrodynamic equations with zero magnetic diffusivity and ill-prepared initial data in three-dimensional bounded domains,…
This work concerns the zero Mach number limit of the compressible primitive equations. The primitive equations with the incompressibility condition are identified as the limiting equations. The convergence with well-prepared initial data…
We prove the incompressible limit of non-isentropic inviscid elastodynamic equations with general initial data in 3D half-space. The deformation tensor is assumed to satisfy the neo-Hookean linear elasticity and degenerates in the normal…
We study the incompressible limit of the compressible non-isentropic ideal magnetohydrodynamic equations with general initial data in the whole space $\mathbb{R}^d$ ($d=2,3$). We first establish the existence of classic solutions on a time…