Huicheng Yin

GLOBAL MULTIDIMENSIONAL SHOCK WAVE FOR THE STEADY SUPERSONIC FLOW PAST A THREE-DIMENSIONAL CURVED CONE

In this paper, we establish the global existence and stability of a multidimensional conic shock wave for three-dimensional steady supersonic flow past an infinite cone. The flow is assumed to be hypersonic and described by a steady potential flow equation. Under an appropriate boundary condition on the curved cone, we show that a pointed shock attached at the vertex of the cone will exist globally in the whole space.

On the existence and cusp singularity of solutions to semilinear generalized Tricomi equations with discontinuous initial data

In this paper, we are concerned with the local existence and singularity structures of low regularity solution to the semilinear generalized Tricomi equation with typical discontinuous initial data (u(0, x), ∂tu(0, x)) = (0, φ(x)), where m ∈ ℕ, x = (x1,…,xn), n ≥ 2, and f(t, x, u) is C∞ smooth on its arguments. When the initial data φ(x) is homogeneous of degree zero or piecewise smooth along the hyperplane {t = x1 = 0}, it is shown that the local solution u(t, x) ∈ L∞([0, T] × ℝn) exists and is C∞ away from the forward cuspidal conic surface or the cuspidal wedge-shaped surfaces respectively. On the other hand, for n = 2 and piecewise smooth initial data φ(x) along the two straight lines {t = x1 = 0} and {t = x2 = 0}, we establish the local existence of a solution and further show that in general due to the degenerate character of the equation under study, where . This is an essential difference to the well-known result for solution to the two-dimensional semilinear wave equation with (v(0, x), ∂tv(0, x)) = (0, φ(x)), where Σ0 = {t = |x|}, and .

Global existence and blowup of smooth solutions of 3-D potential equations with time-dependent damping

In this paper, we are concerned with the global existence and blowup of smooth solutions of the 3-D compressible Euler equation with time-depending damping

Double elliptic equation method and new exact solutions of the (n+1)-dimensional sinh-Gordon equation

\partial_t\rho+\operatorname{div}(\rho u)=0, \quad \partial_t(\rho u)+\operatorname{div}\left(\rho u\otimes u+p\,I_{3}\right)=-\,\frac{\mu}{(1+t)^{\lambda}}\,\rho u, \quad \rho(0,x)=\bar \rho+\varepsilon\rho_0(x),\quad u(0,x)=\varepsilon u_0(x),

Instability of one global transonic shock wave for the steady supersonic Euler flow past a sharp cone

where

Global singularity structure of weak solutions to 3-D semilinear dispersive wave equations with discontinuous initial data☆

x\in\mathbb R^3

On the instability problem of a 3-D transonic oblique shock wave☆

,

Global Multidimensional Shock Waves of 2-Dimensional and 3-Dimensional Unsteady Potential Flow Equations

\mu>0