Weak Solutions to the One-dimensional Non-isentropic Gas Dynamics by the Vanishing Viscosity Method
نویسنده
چکیده
In this paper we consider the non-isentropic equations of gas dynamics with the entropy preserved. Equations are formulated so that the problem is reduced into the 2 2 system of conservation laws with a forcing term in momentum equation. The method of compensated compactness is then applied to prove the existence of weak solution in the vanishing viscosity method.
منابع مشابه
A Self-similar Viscosity Approach for the Riemann Problem in Isentropic Gas Dynamics and the Structure of the Solutions
We study the Riemann problem for the system of conservation laws of one dimensional isentropic gas dynamics in Eulerian coordinates. We construct solutions of the Riemann problem by the method of self-similar zero-viscosity limits, where the self-similar viscosity only appears in the equation for the conservation of momentum. No size restrictions on the data are imposed. The structure of the ob...
متن کاملVanishing Viscosity Limit for Initial-Boundary Value Problems for Conservation Laws
The convergence of the vanishing viscosity method for initialboundary value problems is analyzed for nonlinear hyperbolic conservation laws through several representative systems. Some techniques are developed to construct the global viscous solutions and establish the H−1 compactness of entropy dissipation measures for the convergence of the viscous solutions with general initial-boundary cond...
متن کاملVanishing 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...
متن کاملAdmissibility of weak solutions for the compressible Euler equations, n ≥ 2.
This paper compares three popular notions of admissibility for weak solutions of the compressible isentropic Euler equations of gas dynamics: (i) the viscosity criterion, (ii) the entropy inequality (the thermodynamically admissible isentropic solutions), and (iii) the viscosity-capillarity criterion. An exact summation of the Chapman-Enskog expansion for Grad's moment system suggests that it i...
متن کاملWeak* Solutions II: The Vacuum in Lagrangian Gas Dynamics
We develop a framework in which to make sense of solutions containing the vacuum in Lagrangian gas dynamics. At and near vacuum, the specific volume becomes infinite and enclosed vacuums are represented by Dirac masses, so they cannot be treated in the usual weak sense. However, the weak* solutions recently introduced by the authors can be extended to include solutions containing vacuums. We pr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996