Related papers: Global Steady Subsonic Flows through Infinitely Lo…
For a class of external forces, we prove the existence and uniqueness of smooth transonic flows to the one dimensional steady Euler system with an external force, which is subsonic at the inlet and flows out at supersonic speed after…
In our previous work, we have established the existence of transonic characteristic discontinuities separating supersonic flows from a static gas in two-dimensional steady compressible Euler flows under a perturbation with small total…
This paper concerns the structural stability of subsonic flows with a contact discontinuity in a finitely long axisymmetric cylinder. We establish the existence and uniqueness of axisymmetric subsonic flows with a contact discontinuity by…
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, we study the global existence and asymptotic behavior of classical solutions near vacuum for the initial-boundary value problem modeling isentropic supersonic flows through divergent ducts. The governing equations are the…
The unsteady response of nozzles with steady heat transfer forced by acoustic and/or entropy waves is modelled. The approach is based on the quasi-one-dimensional linearised Euler equations. The equations are cast in terms of three…
In this paper, we consider the one-dimensional isentropic compressible Euler equations with source term $\beta(t,x)\rho|u|^{\alpha}u$ in a bounded domain, which can be used to describe gas transmission in a nozzle.~The model is imposed a…
In this paper we prove existence, uniqueness and regularity of certain perturbed (subsonic--supersonic) transonic potential flows in a two-dimensional Riemannian manifold with "convergent-divergent" metric, which is an approximate model of…
A compactness framework is formulated for the incompressible limit of approximate solutions with weak uniform bounds with respect to the adiabatic exponent for the steady Euler equations for compressible fluids in any dimension. One of our…
The existence, uniqueness, and asymptotic behavior of steady transonic flows past a curved wedge, involving transonic shocks, governed by the two-dimensional full Euler equations are established. The stability of both weak and strong…
The existence and uniqueness of two dimensional steady compressible Euler flows past a wall or a symmetric body are established. More precisely, given positive convex horizontal veloicty in the upstream, there exists a critical value…
In this paper, we study non-Newtonian fluids in a class of unbounded domains with noncompact boundaries. With respect to the resulting mathematical problems, we establish the global existence of solutions with arbitrary large flux under…
We prove the existence of a subsonic weak solution $({\bf u}, \rho, p)$ to steady Euler system in a two-dimensional infinitely long nozzle when prescribing the value of the entropy $(= \frac{p}{\rho^{\gamma}})$ at the entrance by a…
In this paper, we study the initial-boundary value problem of compressible Euler equations with friction and heating that model the combined Fanno-Rayleigh flows through symmetric variable area nozzles, in particular, the case of…
In this paper, both smooth subsonic and transonic flows to steady Euler-Poisson system in a concentric cylinder are studied. We first establish the existence of cylindrically symmetric smooth subsonic and transonic flows to steady…
In this paper we developed an analysis of the compressible, isentropic Euler equations in two spatial dimensions for a generalized polytropic gas law. The main focus is rotational flows in the subsonic regimes, described through the…
This paper concerns the existence of transonic shocks for steady exothermically reacting Euler flows in an almost flat nozzle with the small rate of the exothermic reaction. One of the key points is to quantitatively determine the position…
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…
Considering the isentropic Euler equations of compressible fluid dynamics with geometric effects included, we establish the existence of entropy solutions for a large class of initial data. We cover fluid flows in a nozzle or in spherical…
This paper concerns the structural stability of smooth cylindrically symmetric supersonic spiral flows with large angular velocity for the steady Euler-Poisson system in a concentric cylinder. We establish the existence and uniqueness of…