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赵立丰
单位:数学科学学院
地址:中国科学技术大学数学系
邮编:230026
电话:
个人主页: http://math.ustc.edu.cn/new/teachersinfo1.php?id=78
实验室介绍:
 
个人简历 Personal resume
本人的研究兴趣为色散波方程,只要是来源于量子物理、流体力学、光学中的Schrodinger方程,KdV方程, 波动方程、欧拉方程等。

主要研究方程解的爆破机制、适定性、渐进行为等性质。研究工具主要包括调和分析、变分法及稳定性理论等。
 
研究方向 Research direction
1、非线性色散方程
2、流体力学中的偏微分方程
 
招生信息 Enrollment information
学生应对偏微分方程感兴趣,具备实变函数、泛函分析、数学物理方程等分析类学科的基础知识。
 
论文专著 The monograph
1) Small Data Global Regularity for the 3-D Ericksen–Leslie Hyperbolic Liquid Crystal Model without Kinematic Transport - Siam Journal on Mathematical Analysis - 2021 -
2) On scattering for the cubic defocusing nonlinear Schrödinger equation on the waveguide R2×T - Revista Matemática Iberoamericana - 2020 -
3) Global well-posedness and scattering for mass-critical, defocusing, infinite dimensional vector-valued resonant nonlinear Schrödinger system - SIAM Journal on Mathematical Analysis - 2018 -
4) Asymptotic behaviors of Landau-Lifshitz flows from R2 to Kähler manifolds - Calculus of Variations and Partial Differential Equations - 2017 -
5) Asymptotic stability of harmonic maps between 2D hyperbolic spaces under the wave map equation. II. Small energy case - Dynamics of Partial Differential Equations - 2018 -
6) Isometric decomposition operators, function spaces and applications to nonlinear evolution equations - J. Func. Anal. - 2006 - Vol. 233, No. 1
7)  Global well-posedness and scattering for the energy-critical defocusing Hartree equation for radial data - J. Func. Anal. - 2007 - Vol. 253
8) Global well-posedness and scattering for the mass-critical Hartree equation with radial data - J. Math. Pure. Appl. - 2009 - Vol. 91
9) Global wellposedness and scattering for the focusing energy-critical nonlinear Schrodinger equations of fourth order in the radial case - J. Diff. Equa - 2009 - Vol. 246
10) Global well-posedness and scattering for the defocusing H^{\frac{1}{2}} -subcritical Hartree equation in R^d - Ann. I. H. Poincaré – Analyse Non Lineaire - 2009 - Vol. 26
11) On the blow-up phenomenon for the mass-critical focusing Hartree equation in R^4 - Colloq. Math. - 2010 - Vol. 119
12) Global well-posedness and scattering for the energy-critical, defocusing Hartree equation in R1+n - Comm. PDE - 2011 - Vol. 36
 
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