教学情况:本科生课程:常微分方程、线性代数、概率统计、微积分。
研究领域:偏微分方程专业,主要研究方向为流体力学。利用傅里叶分析(调和分析)、函数空间理论(Besov空间、Weak-Herz空间、BMO空间等)、半群理论和偏微分经典方法解决具有物理学、化学、材料学、生物学等实际背景的各类可压缩与不可压缩流体耦合方程组的基本数学问题。例如,方程组弱解、强解、温和解与经典解的存在唯一性、正则性、长时间行为和衰减率,以及在各类临界次空间解的整体适定性等问题。
科研项目:
(1)不可压磁粘弹性流体的数学研究,国家自然科学基金(青年项目),项目批号:
11801247,2019-2021,经费24万元,项目主持人。
(2)可压缩Navier-Stokes/Cahn-Hilliard方程组的衰减性研究,辽宁省教育厅(青年项目),
项目批准号:L201783639,2017-2020,经费2万元,项目主持人。
发表文章:
Aibo Liu, Changchun Liu, Global classical solutions to the cauchy problem of convective Cahn-Hilliard equation with degenerate diffusion, 2018, accepted. (SCI)
Aibo Liu, Changchun Liu,Global attractorfor a smectic-A liquid crystal modelin in 2D,Bollettino Dellunione Matematica Italiana, 2018(6):1-14. (SCI)
Aibo Liu,Changchun Liu, Global existence of weak solutions to a higher order parabolic system, Bulletin of the Malaysian Mathematical Science,2017(2):1-18.(SCI)
Aibo Liu*,Changchun Liu, Asymptotic dynamics of a new mechanochemical model in biological Patterns, Mathematical Modelling and Analysis, 2017,22(2):252-269.(SCI)
Aibo Liu,Changchun Liu, Cauchy problem for a sixth order Cahn-Hilliard type
equation with inertial term, Evolution Equations and Control Theory,
2015,4(3):315-324.(SCI)
Aibo Liu,Changchun Liu, Weak solutions for a sixth order Cahn-Hilliard type equation with degenerate mobility, Abstract and Applied Analysis, 2014(1):1-7.(SCI)
Changchun Liu,Aibo Liu*,The existence of global attractor for a sixth order parabolic equation, Upb Scientific Bulletin, 2015,76(1),115-128. (SCI)
Changchun Liu,Aibo Liu,Hui Tang,Time-periodic solutions for a driven sixth-order Cahn-Hilliard type equation, Boundary Value Problems, 2013(1):1-17.(SCI)