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：薛留堂

职称：教授

联系方式：xuelt@bnu.edu.cn

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

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, Doubly connected V-states in geophysical models: a general framework. ArXiv:2504.08143. To appear in Calc. Var. Partial Differential Equations (2026).
2. Taoufik Hmidi, Liutang Xue, and Zhilong Xue, Unified theory on V-states structures for active scalar equations. ArXiv:2312.02874. Adv. Math., 486 (2026), Art. No. 110750.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. Piotr B. Mucha and Liutang Xue, Boussinesq system with measure forcing. Mathematische Annalen, 382 (2022), no. 3-4, 1901-1934.
9. Qianyun Miao, Changhui Tan and Liutang Xue, Global regularity for a 1D Euler-alignment system with misalignment. Math. Models Methods Appl. Sci., 31 (2021), no. 3, 473--524.
10. 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.
11. 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.
12. 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.
13. 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.

For the full list of publications, see the homepage http://math0.bnu.edu.cn/~xuelt/.