A Family of Stationary Solutions to the Euler Equations and Generalized Solutions

Weak Solutions to the Stationary Incompressible Euler Equations

Renormalized Solutions of the 2d Euler Equations

In this paper we prove that solutions of the 2D Euler equations in vorticity formulation obtained via vanishing viscosity approximation are renormalized.

Global Solutions of the Relativistic Euler Equations

We demonstrate the existence of solutions with shocks for the equations describing a perfect fluid in special relativity, namely, d i v T = 0, where T ~ = (p + pcZ)ulU j + prl ij is the stress energy tensor for the fluid. Here, p denotes the pressure, u the 4-velocity, p the mass-energy density of the fluid, t/~ the flat Minkowski metric, and c the speed of light. We assume that the equation of...

Stationary and Periodic Solutions of Differential Equations

A stochastic process ξ(t) = ξ(t,ω) (−∞ < t < ∞) with values in R is said to be stationary (in the strict sense) if for every finite sequence of numbers t1, . . . , tn the joint distribution of the random variables ξ(t1 + h), . . . , ξ(tn + h) is independent of h. If we replace the arbitrary number h by a multiple of a fixed number θ , h= kθ (k =±1,±2, . . . ), we get the definition of a periodi...

On Blowup Phenomenon of Solutions to the Euler Equations for Generalized Chaplygin Gas

We obtain some blowup results of the Euler equations for Generalized Chaplygin Gas (GCG). In particular, we show that the solutions with velocity of the form u(t, x) = ȧ(t) a(t) x blow up on finite time if the parameter of the ordinary differential equation related to a(t) is negative. Moreover, by the substitution and perturbation methods, we construct a family of non-spherical symmetric blowu...