In this manuscript, a general formulation of 3-dimensional compressible fluids based on the port-Hamiltonian framework is presented, both for isentropic and non-isentropic assumptions, describing energy flux between mechanical, chemical, thermal domains, with an explicit characterization first second law thermodynamics. For fluids, conversion kinetic into heat by viscous friction considered as ...

We investigate inertial mode oscillations of slowly and uniformly rotating, isentropic, Newtonian stars. Inertial mode oscillations are induced by the Coriolis force due to the star’s rotation, and their characteristic frequencies are comparable with the rotation frequency Ω of the star. So called r-mode oscillations form a sub-class of the inertial modes. In this paper, we use the term “r-mode...

We announce recent results obtained through a combination of asymptotic ODE estimates and numerical Evans function calculations, which together yield stability of isentropic Navier–Stokes shocks for a γ-law gas with 1 ≤ γ ≤ [1, 2.5]. Other γ may be treated similarly.

New exact solutions are obtained for several nonlinear physical equations, namely the Navier–Stokes and Euler systems, an isentropic compressible fluid system and a vector nonlinear Schrödinger equation. The solution methods make use of the symmetry group of the system in situations when the standard Lie method of symmetry reduction is not applicable.

A simple model is presented for the time-averaged electron mobility within a Hall thruster. The model is predicated on the experimental evidence for isentropic electron flow and, when used in a one-dimensional simulation, captures plasma properties that are in reasonable agreement with experiment.

We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a strong solution so that it is unique in a class of weak solutions. Known weak-strong uniqueness results are improved. Classical uniqueness results for this equation follow naturally.

Abstract: We prove the existence of global weak solutions to the Navier-Stokes equations for compressible isentropic fluids for any γ > 1 when the Cauchy data are helically symmetric, where the constant γ is the specific heat ratio. Moreover, a new integrability estimate of the density in any neighborhood of the symmetry axis (the singularity axis) is obtained.

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.

We consider a semidiscrete kinetic scheme for the isentropic gas dynamic system with γ = 3 which corresponds exactly to the “transport-collapse method” of Brenier. We show the existence of shock profiles for every admissible limit values. In addition we give properties of such profiles.