Related papers: Three dimensional spherical transonic shock in a h…
We are concerned with the structural stability of conical shocks in the three-dimensional steady supersonic flows past Lipschitz perturbed cones whose vertex angles are less than the critical angle. The flows under consideration are…
Shock waves are steep wave fronts that are fundamental in nature, especially in high-speed fluid flows. When a shock hits an obstacle, or a flying body meets a shock, shock reflection/diffraction phenomena occur. In this paper, we show how…
For the three-dimensional steady non-isentropic compressible Euler system with friction, we show existence of a class of symmetric subsonic, supersonic and transonic-shock solutions in a straight duct with constant square-section. Such…
Under increasing compression, an unbuckled shell is in a metastable state which becomes increasingly precarious as the buckling load is approached. So to induce premature buckling a lateral disturbance will have to overcome a decreasing…
We are concerned with global solutions of multidimensional Riemann problems for nonlinear hyperbolic systems of conservation laws, focusing on their global configurations and structures. We present some recent developments in the rigorous…
We study the uniqueness of solutions with a transonic shock in a two-dimensional Riemannian manifold with a special metric, which can be regarded as an approximate model of the general physical nozzles, within a class of transonic shock…
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…
We establish the stability of 3-D axisymmetric transonic shock solutions of the steady full Euler system in divergent nozzles under small perturbations of an incoming radial supersonic flow and a constant pressure at the exit of the…
We establish a variational inequality formulation that captures the transonic shock for a steady compressible potential flow. Its critical point satisfies the transonic equation; moreover the associated jump conditions across its free…
Transonic buffet is commonly associated with self-sustained flow unsteadiness involving shock-wave/boundary-layer interaction over aerofoils and wings. The phenomenon has been classified as either laminar or turbulent based on the state of…
The dynamic evolution of a highly underexpanded transient supersonic jet at the exit of a pulse detonation engine is investigated via high-resolution time-resolved schlieren and numerical simulations. Experimental evidence is provided for…
In this paper, the steady inviscid flows with radial symmetry for the isothermal Euler system are studied in an annulus. We present a complete classification of transonic radially symmetric flow patterns in term of physical boundary…
The interaction between a supersonic stellar wind and a (super-)sonic interstellar wind has recently been viewed with new interest. We here first give an overview of the modeling, which includes the heliosphere as an example of a special…
We integrate for the first time the hydrodynamic Hall-Vinen-Bekarevich-Khalatnikov equations of motion of a $^{1}S_{0}$-paired neutron superfluid in a rotating spherical shell, using a pseudospectral collocation algorithm coupled with a…
The general problem of shock formation in three space dimensions was solved by D. Christodoulou in his 2007 monograph: 'The Formation of Shocks in 3-dimensional Fluids'. In this work also a complete description of the maximal development of…
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 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…
We numerically examine the mechanisms that describe the shock-boundary layer interactions in transonic flow past an oscillating wing section. At moderate and high angles of incidence but low amplitudes of oscillation, shock induced flow…
The subject of this work is the shock development problem in fluid mechanics. A shock originates from an acoustically spacelike surface in spacetime at which the 1st derivatives of the physical variables blow up. The solution requires the…
We prove global in time dynamical stability of steady transonic shock solutions in divergent quasi-one-dimensional nozzles. We assume neither the smallness of the relative slope of the nozzle nor the weakness of the shock. Key ingredients…