Using the symbol calculus developed by Berezin, Kree and Raczka, it is shown that the algebra generated by the canonical commutation relation (CCR) is splitted into creation part and annhilation part with holomorphic ...Using the symbol calculus developed by Berezin, Kree and Raczka, it is shown that the algebra generated by the canonical commutation relation (CCR) is splitted into creation part and annhilation part with holomorphic and anti-bolomorphic symbols respectively. Further. in the Weyl representation of CCR, three Weyl operators will constitute an irreducible set of the fall CCR-algebra if some number theoretic conditions are satisfied.展开更多
In this article we study the Gevrey regularization effect for the spatially inhomogeneous Boltzmann equation without angular cut-off.This equation is partially elliptic in the velocity direction and degenerates in the...In this article we study the Gevrey regularization effect for the spatially inhomogeneous Boltzmann equation without angular cut-off.This equation is partially elliptic in the velocity direction and degenerates in the spatial variable.We consider the nonlinear Cauchy problem for the fluctuation around the Maxwellian distribution and prove that any solution with mild regularity will become smooth in the Gevrey class at positive time with the Gevrey index depending on the angular singularity.Our proof relies on the symbolic calculus for the collision operator and the global subelliptic estimate for the Cauchy problem of the linearized Boltzmann operator.展开更多
文摘Using the symbol calculus developed by Berezin, Kree and Raczka, it is shown that the algebra generated by the canonical commutation relation (CCR) is splitted into creation part and annhilation part with holomorphic and anti-bolomorphic symbols respectively. Further. in the Weyl representation of CCR, three Weyl operators will constitute an irreducible set of the fall CCR-algebra if some number theoretic conditions are satisfied.
基金supported by National Natural Science Foundation of China(Grant No.11631011)supported by National Natural Science Foundation of China(Grant Nos.11961160716,11871054 and 11771342)+1 种基金the Natural Science Foundation of Hubei Province(Grant No.2019CFA007)the Fundamental Research Funds for the Central Universities(Grant No.2042020kf0210)。
文摘In this article we study the Gevrey regularization effect for the spatially inhomogeneous Boltzmann equation without angular cut-off.This equation is partially elliptic in the velocity direction and degenerates in the spatial variable.We consider the nonlinear Cauchy problem for the fluctuation around the Maxwellian distribution and prove that any solution with mild regularity will become smooth in the Gevrey class at positive time with the Gevrey index depending on the angular singularity.Our proof relies on the symbolic calculus for the collision operator and the global subelliptic estimate for the Cauchy problem of the linearized Boltzmann operator.
