C 0 Approximation on the Spatially Homogeneous Boltzmann Equation for Maxwellian Molecules

نویسنده

  • Minling Zheng
چکیده

In this paper we study the viscosity analysis of the spatially homogeneous Boltzmann equation for Maxwellian molecules. We first show that the global existence in time of the mild solution of the viscosity equation ( , ) t v f Q f f f          . We then study the asymptotic behaviour of the mild solution as the coefficients 0    , and an estimate on 0 f f   is derived.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Second Order Scheme for the Spatially Homogeneous Boltzmann Equation with Maxwellian Molecules

In the standard approach, particle methods for the Boltzmann equation are obtained using an explicit time discretization of the spatially homogeneous Boltzmann equation. This kind of discretization leads to a restriction on the discretization parameter as well as on the diierential cross section in the case of the general Boltzmann equation. Recently, it was shown, how to construct an implicit ...

متن کامل

Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation

For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution, provided the initial data have a Maxwellian upper bound. The main technique is based on a comparison principle that uses a certain dissipative property of the linear Boltzmann equation. Implications of the technique t...

متن کامل

Gelfand-shilov Smoothing Properties of the Radially Symmetric Spatially Homogeneous Boltzmann Equation without Angular Cutoff

We prove that the Cauchy problem associated to the radially symmetric spatially homogeneous non-cutoff Boltzmann equation with Maxwellian molecules enjoys the same Gelfand-Shilov regularizing effect as the Cauchy problem defined by the evolution equation associated to a fractional harmonic oscillator.

متن کامل

On Large Deviations for Particle Systems Associated with Spatially Homogeneous Boltzmann Type Equations

We consider a dynamical interacting particle system whose empirical distribution tends to the solution of a spatially homogeneous Boltzmann type equation, as the number of particles tends to infinity. These laws of large numbers were proved for the Maxwellian molecules by H. Tanaka ([Ta1]) and for the hard spheres by A.S. Sznitman ([Sz1]). In the present paper we investigate the corresponding l...

متن کامل

The Landau Equation for Maxwellian Molecules and the Brownian Motion on Son (r)

In this paper we prove that the spatially homogeneous Landau equation for Maxwellian molecules can be represented through the product of two elementary processes. The first one is the Brownian motion on the group of rotations. The second one is, conditionally on the first one, a Gaussian process. Using this representation, we establish sharp multi-scale upper and lower bounds for the transition...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2011