5 papers
Backward Uniqueness for Coupled Ultraparabolic Operators and an Application to Jerk-Driven Control Models
Xiao-Dong Cao, Chao-Jiang Xu, Yan Xu
We prove backward uniqueness for a class of ultraparabolic operators with coupled linear drift. The main difficulty is that the Fourier transform in the degenerate variables turns…
Analytic smoothing effect for a model of Kolmogorov-Prandtl type equations
Xiao-Dong Cao, Chao-Jiang Xu, Yan Xu
In this note, we consider the Cauchy problem for a model of Kolmogorov-Prandtl type equations. For the small perturbation of a constant state, we prove that it admits a unique clas…
The Gevrey Gelfand-Shilov regularizing effect of the Landau equation with soft potential
Xiao-Dong Cao, Chao-Jiang Xu, Yan Xu
This paper studies the Cauchy problem for the spatially inhomogeneous Landau equation with soft potential in the perturbative framework around the Maxwellian distribution. Under a…
Regularizing effect of the spatially homogeneous Landau equation with soft potential
Xiao-Dong Cao, Chao-Jiang Xu, Yan Xu
This paper investigates the Cauchy problem of the spatially homogeneous Landau equation with soft potential under the perturbation framework to global equilibrium. We prove that th…
Analytic smoothing effect of the Cauchy problem for a class of ultra-parabolic equations
Xiao-Dong Cao, Chao-Jiang Xu
In this paper, we study a class of strongly degenerate ultraparabolic equations with analytic coefficients. We demonstrate that the Cauchy problem exhibits an analytic smoothing ef…