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刘桥

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刘桥,理学博士

(一) 主要经历
2014年8月至2016年8月,北京应用物理与计算数学研究所,在职博士后,导师:江松研究员;

2013年7月至8月访问浙江大学数学系(张挺教授);

2012年7月至今,湖南师范大学数学系,教师;

2012年6月获中山大学基础数学博士学位(导师:崔尚斌教授,博士论文:关于不可压磁流体动力学方程组若干问题的研究),并进入湖南师范大学数学系工作至今;

2008年11月至2009年5月上海杉达学院光彪学院教师;

2008年6月获兰州大学应用数学硕士学位(导师:范先令教授,硕士论文:带权变指数Soblev空间W^{1,p(x)}(\Omega,v_{0},v_{1})的紧迹嵌入);

2005年6月获天水师范学院理学学士学位.

(二)研究方向: 非线性偏微分方程

主要研究领域为非线性泛函分析与流体中偏微分方程, 这其中最感兴趣的研究方向是不可压流体方程中MHD方程组,不可压向列型液晶流方程组等.

(三)科研项目情况

[1] 参与国家自然科学基金“生物学和物理学中的一些偏微分方程问题”, 项目负责人: 崔尚斌,项目号:11171357,项目时间:
2012.01—2014.12.

[2] 参与国家青年基金“两类两个分支的Camassa-Holm系统的弱解问题”, 项目负责人: 关春霞,项目号:11201494,项目时间:
2012.01—2014.12.

[3] 主持湖南省青年基金“不可压磁流体动力学模型与向列型液晶流模型若干问题的研究”,项目号:13JJ4043
项目时间:2013.01-2015.12

[4] 主持国家天元基金“不可压磁流体动力学方程组若干问题的研究”,项目号:11326155
项目时间:2014.01-2014.12

[5] 主持国家青年基金“不可压向列型液晶流系统的一些数学问题研究", 项目号:11401202
项目时间:2015.01-2017.12

(四)主讲课程:

主讲过的本科生公共基础课: 高等数学,经济数学等; 目前承担本科课程:实变函数与高等数学

主讲过研究生课程: 偏微分方程

(五)主要论著

[1] Q. Liu, Existence of three solutions for $p(x)$-Laplacian equations, Nonlinear Anal., 68 (2008),
2119--2127.

[2] Q. Liu, Compact trace in weighted variable exponent Sobolev spaces,J. Math. Anal. Appl.,348 (2008),
760--774.

[3] Q. Liu and S. Cui, Regularity of solutions to 3-Dnematic liquid crystal flows, Electro. J. Diff. Eqns.,
173 (2010), 1--5.

[4] Q. Liu, J. Zhao and S. Cui, A regularity criterion for the three-dimensional nematic liquid crystal flow
in terms of one directional derivative of the velocity, J. Math. Phys.,52 (2011),033102.

[5] Q. Liu, J. Zhao and S. Cui, Existence and regularizing rate estimates of solutions to a generalized
magneto-hydrodynamic system in pseudomeasure spaces, Annali di Matematica Pure ed Applicata, doi:
10.1007/s10231-010-0184-8. (2011).

[6] Q. Liu, J. Zhao and S. Cui, A logarithmically improved regularity criterion for the Navier–Stokes
equations, Monatshefte fur Math., doi: 10.1007/s00605-011 -0 313-5. (2011).

[7] Q. Liu, S. Cui and S. Gala, Logarithmically improved criteria for the 3D nematic liquid crystal flows in
the multiplier spaces, Acta Applicandae Mathematicae, doi: 10.1007/ s10440-011-9653-3. (2011).

[8] Q. Liu and S. Cui, Well-posedness for the incompressible magneto-hydrodynamic system on modulation spaces,
J. Math. Anal. Appl. Doi:10.1016/j.jmaa.2011.12.015.

[9] Q. Liu and S. Cui, Regularizing Rate Estimates for Mild Solutions of the Incompressible Magneto-
hydrodynamic system, Comm. Pure Appl. Anal., 11 (2012), no. 5, 1643–1660.

[10] J. Zhao, Q. Liu and S. Cui, Regularizing and decay rate estimates for solutions to the Cauchy problem of
the Debye-H\"{u}ckel system, Nonlinear Diff. Equa. Appl., doi: 10.1007/ s00030-011-0115-4. (2011).

[11] S. Gala, Q, Liu and M. A. Ragusa, A new regularity criterion for the nematic liquid crystal flows,
Applicable Analysis, doi: 10.1080/00036811.2011.581233. (2011).

[12] J. Zhao, Q. Liu and S. Cui, Global existence and stability for a hydrodynamic system in the nematic
liquid crystal flows, Comm. Pure Appl. Anal., 12 (2013), no. 1, 341–357.

[13] Q.Liu,J.Zhao,S.Cui, Logarithmically improved BKM's criterion for the 3D nematic liquid crystal flows.
Nonlinear Anal. 75 (2012), no. 13, 4942–4949.

[14] Q.Liu,Serrin blow-up criterion for strong solutions to the 3-D compressible nematic liquid crystal flows
with vacuum. Electron. J. Differential Equations 2013, No. 107, 22 pp.

[15] Q.Liu,J.Zhao, A regularity criterion for the solution of nematic liquid crystal flows in terms of the
$\dot{B}^{-1}_{\infty,\infty}$-norm. J. Math. Anal. Appl. 407 (2013), no. 2, 557–566.

[16] Q.Liu,P.Zhang,S.Gala, Logarithmically improved criteria for the 3D nematic liquid crystal flows in the
Morrey–Campanato space. Comput. Math. Appl. 66 (2013), no. 11, 2327–2334.

[17] Q.Liu, J.Zhao,Logarithmically improved blow-up criteria for the nematic liquid crystal flows. Nonlinear
Anal. Real World Appl. 16 (2014), 178–190.

[18] Q.Liu, Serrin blow-up criterion for strong solutions to the 3-D compressible nematic liquid crystal
flows with vacuum. Electron. J. Differential Equations 2013, No. 107, 22 pp.

[19] Q.Liu, D. Liu, Existence and multiplicity of solutions to a p(x)-Laplacian equation with nonlinear
boundary condition on unbounded domain. Differ. Equ. Appl. 5 (2013), no. 4, 595–611.

[20] J.Zhao,Q. Liu, Logarithmically improved regularity criterion for the 3D generalized magneto-
hydrodynamic equations. Acta Math. Sci. Ser. B Engl. Ed. 34 (2014), no. 2, 568–574.

[21] J.Zhao,Q. Liu, On the Cauchy problem for the fractional drift-diffusion system in critical Besov
paces. Appl. Anal. 93 (2014), no. 7, 1431–1450.

[22] Q. Liu, Well-posedness for the Nematic Liquid Crystal Flow with Rough Initial Data, To appear Chinese
Annal. Math. Ser. A.

[23] Q. Liu, J.Zhao, Global well-posedness for the generalized magneto-hydrodynamic equations in the
critical Fourier-Herz spaces, J. Math. Anal. Appl., 420 (2014),1301—1315.

[24] Q. Liu, J.Zhao, S. Cui, Existence and Regularizing Rate Estimates of Mild Solutions to a Generalized
Magneto-hydrodynamic System in $Q$-Spaces, To appear Asian-European Journal of Mathematics.

[25] Q.Liu, A regularity criterion for the Navier-Stokes equations in terms of one directional derivative of
the velocity, Acta. Appl. Math.,(2014), Doi 10.1007/s10440-014-9975-z.

[26] Q.Liu,Space-time regularity of the mild solutions to the incompressible generalized Navier-Stokes
equations with small rough initial data, Nonlinear Analysis:Real World Applications, 22 (2015),373—387.

[27] Q.Liu,T.Zhang,J.Zhao,Global solutions to the 3D incompressible nematic liquid crystal system,
J.Differential Equations (2015),http://dx.doi.org/10.1016/j.jde.2014.11.002.

[28] Q. Liu, On the temperal decay of solutions to the two-dimensional nematic liquid crystal flows, To
appear Mathematische Nachrichten, (2015).

近期发表的代表性论文: 

Q. Liu, C. Dou, Incompressible limit of the compressible nematic liquid crystal flows in a bounded domain with perfectly conducting boundary, Submitted.

Q. Liu, Global well-posedness and termporal decay estimates for the 3D nematic liquid crystal flows, Submitted.

Q. Liu, Y. Wei, Blow up criteria for the incompressible nematic liquid crystal flows, to appear Acta Applicandae Mathematicae.

Q. Liu, S. Liu, W. Tan, X. Zhong, Global well-posedness of the 2D nonhomogeneous incompressible nematic liquid crystal flows, J. Differential Equations, DOI 10.1016/j.jde.2016.08.44

Q. Liu, On weak--strong uniqueness of solutions to the generalized incompressible Navier--Stokes equations. Comput. Math. Appl., 72 (2016), no. 3, 675--686.

Q. Liu, Gevrey analyticity of solutions to the 3D nematic liquid crystal flows in critical Besov space. Nonlinear Anal. Real World Appl., 31 (2016), 431--451.

Q. Liu, On the temporal decay of solutions to the two-dimensional nematic liquid crystal flows. Math. Nachr., 289 (2016), no. 5-6, 678--692.

Q. Liu, T. Zhang, J. Zhao, Well-posedness for the 3D incompressible nematic liquid crystal system in the critical $L^p$ framework. Discrete Contin. Dyn. Syst., 36 (2016), no. 1, 371--402.

Q. Liu, On blow-up criteria for the 3D nematic liquid crystal flows. IMA J. Appl. Math., 80 (2015), no. 6, 1855--1870.

Q. Liu, A regularity criterion for the Navier-Stokes equations in terms of one directional derivative of the velocity. Acta Appl. Math., 140 (2015), 1--9.

Q. Liu, J. Zhao, S. Cui, Existence and regularizing rate estimates of mild solutions to a generalized magneto-hydrodynamic system in Q-spaces. Asian-Eur. J. Math., 8 (2015), no. 3, 1550049, 20 pp.

Q. Liu, Space-time derivative estimates of the Koch-Tataru solutions to the nematic liquid crystal system in Besov spaces. J. Differential Equations, 258 (2015), no. 12, 4368--4397.

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