Free boundary problems in shock reflection/diffraction and related transonic flow problems

Free boundary problems in shock reflection/diffraction and related transonic flow problems.

Shock waves are steep wavefronts 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 several long-standing shock reflection/diffraction problems can be formulated as free boundary problems, discuss some recent progress in developing mathematic...

Transonic shocks and free boundary problems for the full Euler equations in infinite nozzles

We establish the existence, stability, and asymptotic behavior of transonic flows with a transonic shock for the steady, full Euler equations in two-dimensional infinite nozzles of slowly varying cross-sections. Given a smooth incoming flow that is close to a uniform supersonic state at the entrance, we prove that there exists a transonic flow whose infinite downstream smooth subsonic region is...

On Free Boundary Problems

Free Boundary Problems

Paradigmatic examples are the classical Stefan problem and more general models of phase transitions, where the free boundary is the moving interface between phases. Other examples come from problems in surface science, plastic molding and glass rolling, filtration through porous media, where free boundaries occur as fronts between saturated and unsaturated regions, and others from reaction-diff...

Multidimensional Transonic Shocks and Free Boundary Problems for Nonlinear Equations of Mixed Type

We are concerned with the existence and stability of multidimensional transonic shocks for the Euler equations for steady potential compressible fluids. The Euler equations, consisting of the conservation law of mass and the Bernoulli law for the velocity, can be written as the following second-order nonlinear equation of mixed elliptic-hyperbolic type for the velocity potential φ : Ω ⊂ R → R: ...