Formation of singularity and smooth wave propagation for the non-isentropic compressible Euler equations
نویسنده
چکیده
We define compressive and rarefactive waves and give the differential equations describing smooth wave steepening for the compressible Euler equations with a varying entropy profile and general pressure laws. Using these differential equations, we directly generalize P. Lax’s singularity (shock) formation results in [9] for hyperbolic systems with two variables to the 3× 3 compressible Euler equations for a polytropic ideal gas. Our results are valid globally without restriction on the size of the variation of initial data.
منابع مشابه
The Formation of Shock Waves in the Presence of Vorticity
In his 2007 monograph, D. Christodoulou proved a breakthrough result giving a complete description of the formation of shock waves, starting from small, regular initial conditions, in solutions to the relativistic Euler equations. In 2014, Christodoulou–Miao extended the result to the nonrelativistic compressible Euler equations. In both works, the assumptions on the initial conditions caused t...
متن کاملWell-posedness for compressible Euler equations with physical vacuum singularity
An important problem in the theory of compressible gas flows is to understand the singular behavior of vacuum states. The main difficulty lies in the fact that the system becomes degenerate at the vacuum boundary, where the characteristics coincide and have unbounded derivative. In this paper, we overcome this difficulty by presenting a new formulation and new energy spaces. We establish the lo...
متن کاملGlobal existence of smooth solutions to two-dimensional compressible isentropic Euler equations for Chaplygin gases
In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for two-dimensional flow of Chaplygin gases.
متن کاملOn Isentropic Approximations for Compressible Euler Equations
In this paper, we first generalize the classical results on Cauchy problem for positive symmetric quasilinear systems to more general Besov space. Through this generalization, we obtain the local well-posedness with initial data in the space B d 2 +1 2,1 (R ) which has critical regularity index. We then apply these results to give an explicit characterization on the Isentropic approximation for...
متن کاملWell-posedness for compressible Euler with physical vacuum singularity
An important problem in the theory of compressible gas flows is to understand the singular behavior of vacuum states. The main difficulty lies in the fact that the system becomes degenerate at the vacuum boundary, where the characteristics coincide and have unbounded derivative. In this paper, we overcome this difficulty by presenting a new formulation and new energy spaces. We establish the lo...
متن کامل