Beltrami States for Compressible Barotropic Flows

Lagrangian Averaging, Nonlinear Waves, and Shock Regularization

In this thesis, we explore various models for the flow of a compressible fluid as well as model equations for shock formation, one of the main features of compressible fluid flows. We begin by reviewing the variational structure of compressible fluid mechanics. We derive the barotropic compressible Euler equations from a variational principle in the material frame. The particle relabeling symme...

Blow up of smooth solutions to the barotropic compressible magnetohydrodynamic equations with finite mass and energy

We prove that the smooth solutions to the Cauchy problem for the three-dimensional compressible barotropic magnetohydrodynamic equations with conserved total mass and finite total energy lose the initial smoothness within a finite time. Further, we show that the same result holds for the solution to the Cauchy problem for the multidimensional compressible NavierStokes system. Moreover, for the ...

Nonlinear Acoustics and Shock Formation in Lossless Barotropic Green–naghdi Fluids

The equations of motion of lossless compressible nonclassical fluids under the so-called Green–Naghdi theory are considered for two classes of barotropic fluids: (i) perfect gases and (ii) liquids obeying a quadratic equation of state. An exact reduction in terms of a scalar acoustic potential and the (scalar) thermal displacement is achieved. Properties and simplifications of these model nonli...

A Two -Step Modification toward Implementing Compressible Source Terms in Low Compressible Flows

A free boundary model for Korteweg fluids as a limit of barotropic compressible Navier-Stokes equations

We consider the limit of some barotropic compressible fluid model with Korteweg forcing term, studied in [1], as the exponent of the barotropic law goes to infinity. This provides a free boundary problem model, with capillary effects, and therefore generalizes the free boundary model obtained by Lions and Masmoudi [5]. Our interest for such free boundary problem stems from a study of the Leiden...