Formation of δ-Shocks and Vacuum States in the Vanishing Pressure Limit of Solutions to the Euler Equations for Isentropic Fluids

Formation of Delta-shocks and Vacuum States in the Vanishing Pressure Limit of Solutions to the Isentropic Euler Equations

Concentration and cavitation in the vanishing pressure limit of solutions to the Euler equations for nonisentropic fluids

Numerical simulations [2-D Riemann problem in gas dynamics and formation of spiral, in: Nonlinear Problems in Engineering and Science—Numerical and Analytical Approach (Beijing, 1991), Science Press, Beijing, 1992, pp. 167–179; Discrete Contin. Dyn. Syst. 1 (1995) 555–584; 6 (2000) 419–430] for the Euler equations for gas dynamics in the regime of small pressure showed that, for one case, the p...

Vanishing Viscosity Limit of the Navier-Stokes Equations to the Euler Equations for Compressible Fluid Flow

We establish the vanishing viscosity limit of the Navier-Stokes equations to the isentropic Euler equations for one-dimensional compressible fluid flow. For the NavierStokes equations, there exist no natural invariant regions for the equations with the real physical viscosity term so that the uniform sup-norm of solutions with respect to the physical viscosity coefficient may not be directly co...

The Cauchy Problem on the Compressible Two-fluids Euler-Maxwell Equations

In this paper, we are concerned with the Cauchy problem on the compressible isentropic two-fluids Euler-Maxwell equations in three dimensions. The global existence of solutions near constant steady states with the vanishing electromagnetic field is established, and also the time-decay rates of perturbed solutions in L space for 2 ≤ q ≤ ∞ are obtained. The proof for existence is due to the class...

Existence Theory for the Isentropic Euler Equations

We establish an existence theorem for entropy solutions to the Euler equations modeling isentropic compressible fluids. We develop a new approach for constructing mathematical entropies for the Euler equations, which are singular near the vacuum. In particular, we identify the optimal assumption required on the singular behavior on the pressure law at the vacuum in order to validate the two-ter...