Global classical solutions near Maxwellians are constructed for the Boltzmann equation in a periodic box with angular soft cutoff, that is, -3 〈 γ 〈 0. The construction of global solution is based on an energy meth...Global classical solutions near Maxwellians are constructed for the Boltzmann equation in a periodic box with angular soft cutoff, that is, -3 〈 γ 〈 0. The construction of global solution is based on an energy method used in [9].展开更多
In this paper, we combine the method of constructing the compensating function introduced by Kawashima and the standard energy method for the study on the Landau equation with external forcing. Both the global existen...In this paper, we combine the method of constructing the compensating function introduced by Kawashima and the standard energy method for the study on the Landau equation with external forcing. Both the global existence of solutions near the time asymptotic states which are local Maxwellians and the optimal convergence rates are obtained. The method used here has its own advantage for this kind of studies because it does not involve the spectrum analysis of the corresponding linearized operator.展开更多
In either a periodic box Td or Rd （1 ≤ d ≤ 3）, we obtain global bounded solution of the relativistic Boltzmann equation near global relativistic Maxwellian, in terms of natural mass, energy conservation and the en...In either a periodic box Td or Rd （1 ≤ d ≤ 3）, we obtain global bounded solution of the relativistic Boltzmann equation near global relativistic Maxwellian, in terms of natural mass, energy conservation and the entropy inequality.展开更多
The existence and uniqueness of positive solutions for a class of quasilinear ordinary differential equations with a large parameter are obtained. It is shown that the flat core of positive solutions can exist. So som...The existence and uniqueness of positive solutions for a class of quasilinear ordinary differential equations with a large parameter are obtained. It is shown that the flat core of positive solutions can exist. So some results of [1-3] are sharpened.展开更多
文摘Global classical solutions near Maxwellians are constructed for the Boltzmann equation in a periodic box with angular soft cutoff, that is, -3 〈 γ 〈 0. The construction of global solution is based on an energy method used in [9].
基金supported by Strategic Research Grant of City University of Hong Kong, 7002129the Changjiang Scholar Program of Chinese Educational Ministry in Shanghai Jiao Tong University+1 种基金The research of the second author was supported partially by NSFC (10601018)partially by FANEDD
文摘In this paper, we combine the method of constructing the compensating function introduced by Kawashima and the standard energy method for the study on the Landau equation with external forcing. Both the global existence of solutions near the time asymptotic states which are local Maxwellians and the optimal convergence rates are obtained. The method used here has its own advantage for this kind of studies because it does not involve the spectrum analysis of the corresponding linearized operator.
文摘In either a periodic box Td or Rd （1 ≤ d ≤ 3）, we obtain global bounded solution of the relativistic Boltzmann equation near global relativistic Maxwellian, in terms of natural mass, energy conservation and the entropy inequality.
文摘The existence and uniqueness of positive solutions for a class of quasilinear ordinary differential equations with a large parameter are obtained. It is shown that the flat core of positive solutions can exist. So some results of [1-3] are sharpened.
