Multidimensional Transonic Shocks and Free Boundary Problems for Nonlinear Equations of Mixed Type Gui-qiang Chen and Mikhail Feldman
نویسنده
چکیده
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: (1.1) div (ρ(|Dφ|)Dφ) = 0, where the density function ρ(q) is
منابع مشابه
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: ...
متن کاملShock Reflection-Diffraction Phenomena and Multidimensional Conservation Laws
When a plane shock hits a wedge head on, it experiences a reflectiondiffraction process, and then a self-similar reflected shock moves outward as the original shock moves forward in time. The complexity of reflection-diffraction configurations was first reported by Ernst Mach in 1878, and experimental, computational, and asymptotic analysis has shown that various patterns of shock reflection-di...
متن کاملTransonic 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...
متن کاملPotential theory for shock reflection by a large-angle wedge.
When a plane shock hits a wedge head on, it experiences a reflection, and then a self-similar reflected shock moves outward as the original shock moves forward in time. Experimental, computational, and asymptotic analysis has shown that various patterns of reflected shocks may occur, including regular and Mach reflection. However, most fundamental issues for shock reflection phenomena have not ...
متن کاملShock Reflection-Diffraction and Nonlinear Partial Differential Equations of Mixed Type
We present our recent results on the existence and regularity of shock reflectiondiffraction configurations by a wedge up to the sonic wedge angle, which is the von Neumann sonic conjecture. The problem is first formulated as a boundary value problem for a second-order nonlinear partial differential equation of mixed hyperbolic-elliptic type in an unbounded domain. Then the boundary value probl...
متن کامل