Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation (2009)
Lekrine, Nadia, Xu, Chao-Jiang
In this work, we consider a spatially homogeneous Kac's equation with a non cutoff cross section. We prove that the weak solution of the Cauchy problem is in the Gevrey class for positive time. This...
Gevrey Regularity for Solution of the Spatially Homogeneous Landau Equation (2009)
Chen, Hua, Li, Weixi, Xu, Chao-Jiang
In this paper, we study the Gevrey class regularity for solutions of the spatially homogeneous Landau equations in the hard potential case and the Maxwellian molecules case.
Propagation of Gevrey regularity for solutions of Landau equations (2009)
Chen, Hua, Li, Weixi, Xu, Chao-Jiang
By using the energy-type inequality, we obtain, in this paper, the result on propagation of Gevrey regularity for the solution of the spatially homogeneous Landau equation in the cases of Maxwellian...
Gevrey hypoellipticity for a class of kinetic equations (2009)
Chen, Hua, Li, Wei-Xi, Xu, Chao-Jiang
In this paper, we study the Gevrey regularity of weak solutions for a class of linear and semi-linear kinetic equations, which are the linear model of spatially inhomogeneous Boltzmann equations...
Gevrey regularity of subelliptic Monge-Amp\`ere equations in the plane (2009)
Chen, Hua, Li, Wei-Xi, Xu, Chao-Jiang
In this paper, we establish the Gevrey regularity of solutions for a class of degenerate Monge-Amp\`ere equations in the plane, under the assumption that one principle entry of the Hessian is...
Analytic smoothness effect of solutions for spatially homogeneous Landau equation (2009)
Chen, Hua, Li, Wei-Xi, Xu, Chao-Jiang
In this paper, we study the smoothness effect of Cauchy problem for the spatially homogeneous Landau equation in the hard potential case and the Maxwellian molecules case. We obtain the analytic...
Regularizing effect and local existence for non-cutoff Boltzmann equation (2009)
Alexandre, Radjesvarane, Morimoto, Y., Ukai, Seiji, Xu, Chao-Jiang, Yang, Tong
The Boltzmann equation without Grad's angular cutoff assumption is believed to have regularizing effect on the solution because of the non-integrable angular singularity of the cross-section....
The Gevrey Hypoellipticity for linear and non-linear Fokker-Planck equations (2009)
Chen, Hua, Li, Wei-Xi, Xu, Chao-Jiang
In this paper, we study the Gevrey regularity of weak solution for a class of linear and quasilinear Fokker-Planck equations.
Ultra-analytic effect of Cauchy problem for a class of kinetic equations (2009)
Morimoto, Yoshinori, Xu, Chao-Jiang
The smoothing effect of the Cauchy problem for a class of kinetic equations is studied. We firstly consider the spatially homogeneous non linear Landau equation with Maxwellian molecules and...
Ultra-analytic effect of Cauchy problem for a class of kinetic equations (2009)
Morimoto, Yoshinori, Xu, Chao-Jiang
The smoothing effect of the Cauchy problem for a class of kinetic equations is studied. We firstly consider the spatially homogeneous non linear Landau equation with Maxwellian molecules and...
Ultra-analytic effect of Cauchy problem for a class of kinetic equations (2009)
Morimoto, Yoshinori, Xu, Chao-Jiang
The smoothing effect of the Cauchy problem for a class of kinetic equations is studied. We firstly consider the spatially homogeneous non linear Landau equation with Maxwellian molecules and...
The Gevrey Hypoellipticity for linear and non-linear Fokker-Planck equations (2009)
Chen, Hua, Li, Wei-Xi, Xu, Chao-Jiang
In this paper, we study the Gevrey regularity of weak solution for a class of linear and quasilinear Fokker-Planck equations.
The Gevrey Hypoellipticity for linear and non-linear Fokker-Planck equations (2009)
Chen, Hua, Li, Wei-Xi, Xu, Chao-Jiang
In this paper, we study the Gevrey regularity of weak solution for a class of linear and quasilinear Fokker-Planck equations.
Morimoto, Yoshinori, Ukai, Seiji, Xu, Chao-Jiang, Yang, Tong
Most of the work on the Boltzmann equation is based on the Grad's angular cutoff assumption. Even though the smoothing effect from the singular cross-section without the angular cutoff corresponding...
Morimoto, Yoshinori, Ukai, Seiji, Xu, Chao-Jiang, Yang, Tong
Most of the work on the Boltzmann equation is based on the Grad's angular cutoff assumption. Even though the smoothing effect from the singular cross-section without the angular cutoff corresponding...
GEVREY REGULARITY FOR SOLUTION OF THE SPATIALLY HOMOGENEOUS LANDAU EQUATION (2009)
Chen, Hua, Li, Weixi, Xu, Chao-Jiang
In this paper, we study the Gevrey class regularity for solutions of the spatially homogeneous Landau equations in the hard potential case and the Maxwellian molecules case.
Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation (2009)
Lekrine, Nadia, Xu, Chao-Jiang
In this work, we consider a spatially homogeneous Kac's equation with a non cutoff cross section. We prove that the weak solution of the Cauchy problem is in the Gevrey class for positive time. This...
GEVREY REGULARITY FOR SOLUTION OF THE SPATIALLY HOMOGENEOUS LANDAU EQUATION (2009)
Chen, Hua, Li, Weixi, Xu, Chao-Jiang
In this paper, we study the Gevrey class regularity for solutions of the spatially homogeneous Landau equations in the hard potential case and the Maxwellian molecules case.
Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation (2009)
Lekrine, Nadia, Xu, Chao-Jiang
In this work, we consider a spatially homogeneous Kac's equation with a non cutoff cross section. We prove that the weak solution of the Cauchy problem is in the Gevrey class for positive time. This...
Trace theorem on the Heisenberg group (2009)
Bahouri, Hajer, Chemin, Jean-Yves, Xu, Chao-Jiang
We prove in this work the trace and trace lifting theorem for Sobolev spaces on the Heisenberg groups for hypersurfaces with characteristics submanifolds.
Trace theorem on the Heisenberg group (2009)
Bahouri, Hajer, Chemin, Jean-Yves, Xu, Chao-Jiang
We prove in this work the trace and trace lifting theorem for Sobolev spaces on the Heisenberg groups for hypersurfaces with characteristics submanifolds.
Regularizing effect and local existence for non-cutoff Boltzmann equation (2008)
Alexandre, Radjesvarane, Morimoto, Y., Ukai, Seiji, Xu, Chao-Jiang, Yang, Tong
The Boltzmann equation without Grad's angular cutoff assumption is believed to have regularizing effect on the solution because of the non-integrable angular singularity of the cross-section....
Regularizing effect and local existence for non-cutoff Boltzmann equation (2008)
Alexandre, Radjesvarane, Morimoto, Y., Ukai, Seiji, Xu, Chao-Jiang, Yang, Tong
The Boltzmann equation without Grad's angular cutoff assumption is believed to have regularizing effect on the solution because of the non-integrable angular singularity of the cross-section....
Regularizing effect and local existence for non-cutoff Boltzmann equation (2008)
Alexandre, Radjesvarane, Morimoto, Y., Ukai, Seiji, Xu, Chao-Jiang, Yang, Tong
The Boltzmann equation without Grad's angular cutoff assumption is believed to have regularizing effect on the solution because of the non-integrable angular singularity of the cross-section....
Regularizing effect and local existence for non-cutoff Boltzmann equation (2008)
Alexandre, Radjesvarane, Morimoto, Y., Ukai, Seiji, Xu, Chao-Jiang, Yang, Tong
The Boltzmann equation without Grad's angular cutoff assumption is believed to have regularizing effect on the solution because of the non-integrable angular singularity of the cross-section....
Propagation of Gevrey regularity for solutions of Landau equations (2008)
Chen, Hua, Li, Weixi, Xu, Chao-Jiang
By using the energy-type inequality, we obtain, in this paper, the result on propagation of Gevrey regularity for the solution of the spatially homogeneous Landau equation in the cases of Maxwellian...
Propagation of Gevrey regularity for solutions of Landau equations (2008)
Chen, Hua, Li, Weixi, Xu, Chao-Jiang
By using the energy-type inequality, we obtain, in this paper, the result on propagation of Gevrey regularity for the solution of the spatially homogeneous Landau equation in the cases of Maxwellian...
Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations (2007)
Chen, Hua, Li, Wei-Xi, Xu, Chao-Jiang
This paper studies the Gevrey regularity of weak solutions of a class of linear and semilinear Fokker-Planck equations.
The Cauchy problem for viscous shallow water equations (2005)
In this paper we study the Cauchy problem for viscous shallow water equations. We work in the Sobolev spaces of index $s>2$ to obtain local solutions for any initial data, and global solutions for...
The cauchy problem for viscous shallow water equations (2005)
In this paper we study the Cauchy problem for viscous shallow water equations. We work in the Sobolev spaces of index s > 2 to obtain local solutions for any initial data, and global solutions for...
Regularity of weak solutions for a class of infintely degenerate elliptic semilinear equation (2003)