检索结果-南通市图书馆

Existence and gevrey regularity for a two-species chemotaxis system in homogeneous Besov spaces

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2017年第10期60卷 1837-1856页

作者： YANG MingHua FU ZunWei SUN JinYi School of Information Technology Jiangxi University of Finance and Economics Department of Mathematics Linyi University College of Mathematics and Statistics Northwest Normal University

We study the Cauchy problem of a two-species chemotactic model. Using the Fourier frequency localization and the Bony paraproduct decomposition, we establish a unique local solution and blow-up criterion of the solution, when the initial data（u0, v0, w0） belongs to homogeneous Besov spaces B^˙p,1^-2＋3/p（R^3） ×B^˙r,1^-2＋3/r（R^3） ×B^˙q,1^3/q（R^3） for p, q and r satisfying some technical assumptions. Furthermore, we prove that if the initial data is sufficiently small, then the solution is global. Meanwhile, based on the so-called gevrey estimates, we particularly prove that the solution is analytic in the spatial variable. In addition, we analyze the long time behavior of the solution and obtain some decay estimates for higher derivatives in Besov and Lebesgue spaces.

关键词： two-species chemotaxis system gevrey regularity Besov spaces blow-up criterion Triebel-Lizorkin spaces

gevrey regularity and Time Decay of Fractional Porous Medium Equation in Critical Besov Spaces

在线全文

学校读者我要写书评

暂无评论

Journal of Applied Mathematics and Physics 2022年第1期10卷 91-111页

作者： Weiliang Xiao Yu Zhang School of Applied Mathematics Nanjing University of Finance and Economics Nanjing China

In this paper, we show the existence and regularity of mild solutions depending on the small initial data in Besov spaces to the fractional porous medium equation. When 1 α ≤ 2, we prove global well-posedness for initial data with 1 ≤ p q ≤ ∞, and analyticity of solutions with 1 p q ≤ ∞. In particular, we also proved that when α = 1, both u and belong to . We solve this equation through the contraction mapping method based on Littlewood-Paley theory and Fourier multiplier. Furthermore, we can get time decay estimates of global solutions in Besov spaces, which is as t → ∞.

关键词： Well-Posedness gevrey regularity Time Decay Besov Spaces

The gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Science China Mathematics 2022年第3期65卷 443-470页

作者： Hua Chen Xin Hu Wei-Xi Li Jinpeng Zhan School of Mathematics and Statistics Wuhan UniversityWuhan 430072China Computational Science Hubei Key Laboratory Wuhan UniversityWuhan 430072China Department of Mathematics School of ScienceWuhan University of TechnologyWuhan 430070China

In this article we study the gevrey regularization effect for the spatially inhomogeneous Boltzmann equation without angular *** equation is partially elliptic in the velocity direction and degenerates in the spatial *** 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 *** proof relies on the symbolic calculus for the collision operator and the global subelliptic estimate for the Cauchy problem of the linearized Boltzmann operator.

关键词： Boltzmann equation gevrey regularity subelliptic estimate non cut-off symbolic calculus

THE SMOOTHING EFFECT IN SHARP gevrey SPACE FOR THE SPATIALLY HOMOGENEOUS NON-CUTOFF BOLTZMANN EQUATIONS WITH A HARDPOTENTIAL

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2024年第2期44卷 455-473页

作者：刘吕桥曾娟 School of Mathematics and Statistics Anhui Normal UniversityWuhu241002China School of Mathematics and Statistics Wuhan UniversityWuhan430072China

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.

关键词： Boltzmann equation gevrey regularity non-cutoff hard potential

On the Cauchy Problem for Mildly Nonlinear and Non-Boussinesq Case-(ABC) System

在线全文

学校读者我要写书评

暂无评论

Journal of Applied Mathematics and Physics 2024年第4期12卷 1286-1307页

作者： Luhang Zhou School of Mathematical Sciences Chongqing Normal University Chongqing China

In this paper, we investigate the local well-posedness, ill-posedness, and gevrey regularity of the Cauchy problem for Mildly Nonlinear and Non-Boussinesq case-(ABC) system. The local well-posedness of the solution for this system in Besov spaces B p,r s 1 × B p,r s with 1≤p,r≤∞ and s>max{ 1 1 p , 3 2 } was firstly established. Next, we consider the continuity of the solution-to-data map, i.e. the ill-posedness of the solution for this system in Besov space B p,∞ s 1 × B p,∞ s was derived. Finally, the gevrey regularity of the system was presented.

关键词： Local Well-Posedness Ill-Posedness gevrey regularity

Stabilization of Coupled Schrdinger and Heat Equations with Boundary Coupling

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Stabilization of Coupled Schrdinger and Heat Equations wit...