北京师范大学数学科学学院

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薛留堂 Xue Liutang

基本介绍

姓名 (Name)：薛留堂 (Xue Liutang)

职称 (Job Title)：教授 (Professor)

联系方式 (Email)：xuelt@bnu.edu.cn

办公室 (Office): 后主楼 1131

个人主页 (Webpage)：http://math0.bnu.edu.cn/~xuelt/index.html

Curriculum Vitae: (pdf)

Research Interests: Analysis of Partial Differential Equations; Harmonic Analysis.

发表论文与预印本 (Publications and Preprints)

[35] Changhui Tan, Liutang Xue, and Zhilong Xue, A revisit of patch solutions for the 2D Loglog-Euler type equation. ArXiv:2510.18759 [math.AP]. (pdf)

[34] Qianyun Miao, Changhui Tan, Liutang Xue, and Zhilong Xue, Local regularity and finite-time singularity for a class of generalized SQG patches on the half-plane. ArXiv:2410.19273 [math.AP]. (pdf)

[33] Taoufik Hmidi, Liutang Xue, and Zhilong Xue, Doubly connected V-states in geophysical models: a general framework. ArXiv:2504.08143 [math.AP]. Calc. Var. Partial Differential Equations, 65 (2026), Art. No. 137. (pdf)

[32] Taoufik Hmidi, Liutang Xue, and Zhilong Xue, Unified theory on V-states structures for active scalar equations. ArXiv:2312.02874 [math.AP]. Adv. Math., 486 (2026), Art. No. 110750. (pdf)

[31] Omar Lazar, Liutang Xue, and Jiakun Yang, Global regularity and infinite Prandtl number limit of temperature patches for the 2D Boussinesq system. Mathematische Annalen, 392 (2025), 1375--1446. (pdf)

[30] Yatao Li, Qianyun Miao, Changhui Tan, and Liutang Xue, Global well-posedness and refined regularity criterion for the uni-directional Euler-alignment system. International Mathematics Research Notices, 2024 (2024), no. 23, 14393--14422. (pdf)

[29] Xiang Bai, Changhui Tan, and Liutang Xue, Global well-posedness and asymptotic behavior for the Euler-alignment system with pressure. J. Differential Equations, 407 (2024), 269--310. (pdf)

[28] 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. Nonlinearity, 37 (2024), no. 2, paper no. 025007. (pdf)

[27] Omar Lazar, Yatao Li, and Liutang Xue, On the regularity of temperature fronts for the 3D viscous Boussinesq system. Indiana Univ. Math. J., 73 (2024), no. 3, 1005--1060. (pdf)

[26] Taoufik Hmidi, Liutang Xue, and Zhilong Xue, Emergence of time periodic solutions for the generalized surface quasi-geostrophic equation in the disc. Journal of Functional Analysis, 285 (2023), no. 10, Paper No. 110142. (pdf)

[25] 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. (pdf)

[24] 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. (pdf) Erratum. (pdf)

[23] Piotr B. Mucha, and Liutang Xue, Boussinesq system with measure forcing. Mathematische Annalen, 382 (2022), 1901--1934. (pdf)

[22] 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. (pdf)

[21] 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. (pdf)

[20] 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. (pdf)

[19] 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. (pdf)

[18] 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)

[17] 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. (pdf)

[16] 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. (pdf)

[15] 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. (pdf)

[14] 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. (pdf)

[13] Liutang Xue, On the locally self-similar singular solutions for the incompressible Euler equations. Dyn. Partial Differ. Equ. 12 (2015), no. 4, 321--342. (pdf)

[12] Liutang Xue, On the discretely self-similar solutions for the 3D Navier-Stokes equations. Nonlinearity 28 (2015), no. 10, 3695--3708. (pdf)

[11] 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. (pdf)

[10] 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. (pdf)

[9] 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. (pdf)

[8] 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)

[7] 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. (pdf)

[6] 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. (pdf)

[5] 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. (pdf)

[4] 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. (pdf)

[3] 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)

[2] Liutang Xue, Wellposedness and zero microrotation viscosity limit of the 2D micropolar fluid equations. Math. Methods Appl. Sci. 34 (2011), no. 14, 1760--1777. (pdf)

[1] Liutang Xue, On the well-posedness of incompressible flow in porous media with supercritical diffusion. Appl. Anal. 88 (2009), no. 4, 547--561. (pdf)

个人简介

薛留堂，理学博士，教授，博士生导师。2012年于中国工程物理研究院研究生部获得博士学位。2012年9月至2013年8月在法国巴黎东部大学做博士后研究。2013年9月起在北京师范大学工作。2023年3月被聘为教授。主要从事偏微分方程理论方面的研究，尤其是流体力学方程的数学理论的研究。现主持一项国家自然科学基金面上项目。

研究兴趣

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。

科研项目

2015.1-2017.12, 主持一项国家自然科学基金青年基金, No. 11401027.
2018.1-2021.12, 主持一项国家自然科学基金面上项目, No. 11771043.
2023.1-2026.12, 主持一项国家自然科学基金面上项目, No. 12271045.

代表性论著

[1]. Taoufik Hmidi, Liutang Xue, and Zhilong Xue, Unified theory on V-states structures for active scalar equations. Adv. Math., 486 (2026), Art. No. 110750.
[2]. Omar Lazar, Liutang Xue, and Jiakun Yang, Global regularity and infinite Prandtl number limit of temperature patches for the 2D Boussinesq system. Mathematische Annalen, 392 (2025), 1375--1446.
[3]. Yatao Li, Qianyun Miao, Changhui Tan, and Liutang Xue, Global well-posedness and refined regularity criterion for the uni-directional Euler-alignment system. International Mathematics Research Notices, 2024 (2024), no. 23, 14393--14422.
[4]. Taoufik Hmidi, Liutang Xue, and Zhilong Xue, Emergence of time periodic solutions for the generalized surface quasi-geostrophic equation in the disc. Journal of Functional Analysis, 285 (2023), no. 10, Paper No. 110142.
[5]. 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. Erratum. SIAM J. Math. Anal., 56 (2024), no. 6, 8125--8130.
[6]. Piotr B. Mucha and Liutang Xue, Boussinesq system with measure forcing. Mathematische Annalen, 382 (2022), no. 3-4, 1901-1934.
[7]. 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.
[8]. 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.
[9]. 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.