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刘桥
刘桥,理学博士
(一) 主要经历
2014年8月至今,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,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:**,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:**,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:**
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:**
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
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/**.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 Equations2013, 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 MathematischeNachrichten, (2015).
刘桥,理学博士
(一) 主要经历
2014年8月至今,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,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:**,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:**,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:**
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:**
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
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/**.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 Equations2013, 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 MathematischeNachrichten, (2015).