个人简介
Education
2002–2006 B.S. in Mathematics and Applied Mathematics, Zhengzhou University, Henan Province, P. R. China
2006–2009 M.S. in Applied Mathematics, Graduate School of China Academy of Engineering Physics, Beijing, P. R. China (Advisor: Prof. Changxing Miao)
2009–2012 Ph.D. in Applied Mathematics, Graduate School of China Academy of Engineering Physics, Beijing, P. R. China (Advisor: Prof. Changxing Miao)
Academic Positions
2012.9–2013.9 Post-doctor, Laboratoire LAMA, Université Paris-Est, Paris, France (Advisor: Prof. Régis Monneau and Prof. Marco Cannone)
2013.9–2016.9 Assistant Professor, Beijing Normal University, Beijing, P. R. China.
2016.9–present Associate Professor, Beijing Normal University, Beijing, P. R. China.
研究领域
主要研究流体力学方程如Navier-Stokes/Euler 方程、SQG 方程、Boussinesq 系统等的数学理论，主要关注解的整体适定性或者解的有限时刻奇性的问题。所考虑的问题或多或少与千禧年百万美元征题的“三维Navier-Stokes方程光滑解的整体适定性或有限时刻爆破问题”有关联
近期论文
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Taoufik Hmidi, Liutang Xue and Zhilong Xue, Emergence of time periodic solutions for the generalized surface quasi-geostrophic equation in the disc. Submitted, ArXiv:2210.08760 [math.AP].
Xiang Bai, Qianyun Miao, Changhui Tan and Liutang Xue, Global well-posedness and asymptotic behavior in critical spaces for the compressible Euler system with velocity alignment. Submitted, ArXiv:2207.02429 [math.AP].
Omar Lazar, Yatao Li and Liutang Xue, On the regularity of temperature fronts for the 3D viscous Boussinesq system. to appear in Indiana Math. Univ. J., ArXiv:2205.10331 [math.AP].
Yatao Li, Qianyun Miao and Liutang Xue, Global well-posedness for 2D fractional inhomogeneous Navier-Stokes equations with rough density. ArXiv: 2111.12235 [math.AP]. Nonlinearity 36 (2023), 3866--3908.
Dongho Chae, Qianyun Miao and Liutang Xue, Global regularity of non-diffusive temperature fronts for the 2D viscous Boussinesq system. SIAM J. Math. Anal.54 (2022), no. 4, 4043--4103.
Piotr B. Mucha and Liutang Xue, Boussinesq system with measure forcing. Mathematische Annalen,382 (2022), 1901--1934.
Qianyun Miao, Changhui Tan and Liutang Xue, Global regularity for a 1D Euler-alignment system with misalignment. Math. Mod. Meth. Appl. Sci., 31 (2021), no. 3, 473--524.
Qianyun Miao and Liutang Xue, Regularity and singularity results for the dissipative Whitham equation and related surface wave equations. Commun. Math. Sci., 17 (2019), no. 8, 2141--2190.
Omar Lazar and Liutang Xue, Regularity results for a class of generalized surface quasi-geostrophic equations. Journal de Mathématiques Pures et Appliquées, 130 (2019), 200--250.
Piotr B. Mucha, Liutang Xue and Xiaoxin Zheng, Between homogeneous and inhomogeneous Navier-Stokes systems: the issue of stability. J. Differential Equations, 267 (2019), Issue 1, 307--363.
Changxing Miao and Liutang Xue, On the regularity issues of a class of drift-diffusion equations with nonlocal diffusion. SIAM J. Math. Anal., 51 (2019), no. 4, 2927--2970.(pdf)
Qianyun Miao and Liutang Xue, On the Holder regularity of the weak solution to a drift-diffusion equation with pressure. Calc. Var. Partial Differential Equations, 57 (2018), no. 6, Art. 153, 33 pp.
Liutang Xue and Zhuan Ye, On the differentiability issue of the drift-diffusion equation with nonlocal Levy-type diffusion. Pacific J. Mathematics 293 (2018), no. 2, 471--510
Jiahong Wu, Xiaojing Xu, Liutang Xue and Zhuan Ye, Regularity results for the 2D Boussinesq equations with critical or supercritical dissipation. Commun. Math. Sci. 14 (2016), no. 7, 1963--1997.
Liutang Xue, On the locally self-similar solution of the surface quasi-geostrophic equation with decaying or non-decaying profiles. J. Differential Equations 261 (2016), no. 10, 5590--5608.
Liutang Xue, On the locally self-similar singular solutions for the incompressible Euler equations. Dyn. Partial Differ. Equ. 12 (2015), no. 4, 321--342.
Liutang Xue, On the discretely self-similar solutions for the 3D Navier-Stokes equations. Nonlinearity 28 (2015), no. 10, 3695--3708.
Marco Cannone and Liutang Xue, Remarks on self-similar solutions for the surface quasi-geostrophic equation and its generalization. Proc. Amer. Math. Soc. 143 (2015), no. 6, 2613–2622.
Dong Li, Changxing Miao and Liutang Xue, On the well-posedness of a 2D nonlinear and nonlocal system arising from the dislocation dynamics. Commun. Contemp. Math. 16 (2014), no. 2, 1350021, 36 pp.
Xiaojing Xu and Liutang Xue, Yudovich type solution for the 2D inviscid Boussinesq system with critical and supercritical dissipation. J. Differential Equations 256 (2014), no. 9, 3179--3207.
Marco Cannone, Changxing Miao and Liutang Xue, Global regularity for the supercritical dissipative quasi-geostrophic equation with large dispersive forcing. Proc. Lond. Math. Soc. (3) 106 (2013), no. 3, 650--674.(pdf)
Liutang Xue and Xiaoxin Zheng, Note on the well-posedness of a slightly supercritical surface quasi-geostrophic equation. J. Differential Equations 253 (2012), no. 2, 795--813.
Gang Wu and Liutang Xue, Global well-posedness for the 2D inviscid Bénard system with fractional diffusivity and Yudovich's type data. J. Differential Equations 253 (2012), no. 1, 100--125.
Changxing Miao and Liutang Xue, Global well-posedness for a modified critical dissipative quasi-geostrophic equation. J. Differential Equations 252 (2012), no. 1, 792--818.
Changxing Miao and Liutang Xue, On the regularity of a class of generalized quasi-geostrophic equations. J. Differential Equations 251 (2011), no. 10, 2789--2821.
Changxing Miao and Liutang Xue, On the global well-posedness of a class of Boussinesq-Navier-Stokes systems. NoDEA Nonlinear Differential Equations Appl. 18 (2011), no. 6, 707--735.(pdf)
Liutang Xue, Wellposedness and zero microrotation viscosity limit of the 2D micropolar fluid equations. Math. Methods Appl. Sci. 34 (2011), no. 14, 1760--1777.
Liutang Xue, On the well-posedness of incompressible flow in porous media with supercritical diffusion. Appl. Anal. 88 (2009), no. 4, 547--561.
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