In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation e...In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.展开更多
The word “senescence” comes from the Latin senescens, meaning “to begin to age”, and is characterized by a long-lasting but reversible block in proliferation, resulting from stress-induced cell cycle arrest of pre...The word “senescence” comes from the Latin senescens, meaning “to begin to age”, and is characterized by a long-lasting but reversible block in proliferation, resulting from stress-induced cell cycle arrest of previously replication-competent cells.展开更多
基金supported by the NSFC(12101012)the PhD Scientific Research Start-up Foundation of Anhui Normal University.Zeng’s research was supported by the NSFC(11961160716,11871054,12131017).
文摘In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.
基金supported by the Ministry of Science and Innovation and the Spanish Research Agency through FEDER funds (PID2021-1261520B-100) (MICINN/AEI/FEDER, EU)CBM receives an institutional grant from the Fundación Ramón Areces, Spain。
文摘The word “senescence” comes from the Latin senescens, meaning “to begin to age”, and is characterized by a long-lasting but reversible block in proliferation, resulting from stress-induced cell cycle arrest of previously replication-competent cells.
