Formation of singularities of solutions to the three-dimensional Euler–Boltzmann equations in radiation hydrodynamics
نویسندگان
چکیده
Abstract The Cauchy problem for the three-dimensional Euler–Boltzmann equations of a polytropic, ideal and isentropic fluid in radiation hydrodynamics is considered. The formation of singularities in smooth solutions is studied. It is proved that some C1 solutions, regardless of the size of the initial disturbance, will develop singularities in a finite time provided that the initial disturbance satisfies certain conditions.
منابع مشابه
Moving Manifolds in Electromagnetic Fields
We propose dynamic non-linear equations for moving surfaces in an electromagnetic field. The field is induced by a material body with a boundary of the surface. Correspondingly the potential energy, set by the field at the boundary can be written as an addition of four-potential times four-current to a contraction of the electromagnetic tensor. Proper application of the minimal action principle...
متن کاملFormation of Singularities in Three-Dimensional Compressible Fluids
Presented are several results on the formation of singularities in solutions to the three-dimensional Euler equations for a polytropic, ideal fluid under various assumptions on the initial data. In particular, it is shown that a localized fluid which is initially compressed and outgoing, on average, will develop singularities regardless of the size of the initial disturbance. This article prese...
متن کاملLong Time Behavior of Solutions to the 3d Compressible Euler Equations with Damping
The effect of damping on the large-time behavior of solutions to the Cauchy problem for the three-dimensional compressible Euler equations is studied. It is proved that damping prevents the development of singularities in small amplitude classical solutions, using an equivalent reformulation of the Cauchy problem to obtain effective energy estimates. The full solution relaxes in the maximum nor...
متن کاملHydrodynamics of Sieve Tray Distillation Column Using CFD Simulation
Sieve trays are widely used in the gas- liquid contactors such as distillation and absorption towers. In this article, a three-dimensional, two phase CFD model using Euler-Euler framework was developed to simulate a distillation tower with two sieve trays. Hydrodynamic simulation of air and water system in different rates of gas phase was carried out and velocity distribution parameters, clear ...
متن کاملHilbert Expansion from the Boltzmann Equation to Relativistic Fluids
We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of local solutions to the relativistic Boltzmann equation that are nearby the local relativistic Maxwellian constructed from a class of solutions to the relativistic Euler equations that includes a large subclass of near-constant, non-vacuum f...
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 2010