中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：罗天文 助理教授（清华大学）
题 目：Convex integration constructions in fluids dynamics, part I
时 间：2022.07.18（星期一）上午10:00-11:00
地 点：腾讯会议：224-516-848 会议密码：220718
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题 目：Convex integration constructions in fluids dynamics, part II
时 间：2022.07.20（星期三）上午10:00-11:00
地 点：腾讯会议：298-367-621 会议密码：220720
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题 目：Convex integration constructions in fluids dynamics, part III
时 间：2022.08.15（星期一）10:00-11:00
地点：腾讯会议：301-513-107 会议密码：220815
摘 要：We review some of the convex integration constructions in fluid dynamics. Originated in Nash’s work on isometric embedding, the technique has been recently introduced and developed by De Lellis and Szekelyhidi Jr in fluid dynamics. We shall talk about the work on Onsager’s conjecture by Isett and intermittent constructions in Navier-Stokes equations by Buckmaster and Vicol, among others.
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题 目：Some results on admissible weak solutions to the Riemann problem of compressible Euler equations
时 间：2022.08.17（星期三）10:00-11:00
地点：腾讯会议：586-946-466 会议密码：220817
摘 要：We will discuss results on the Riemann problems of compressible Euler equations. This is a joint work with Prof. Zhouping Xin and Chunjing Xie.
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题 目： Some results on weak solutions to The three-dimensional Prandtl equations
时 间：2022.08.19（星期五）10:00-11:00
地点：腾讯会议：274-578-826 会议密码：220819
摘 要：We will talk about our work on weak solutions to three-dimensional Prandtl equations. This is a joint work with Prof. Zhouping Xin.
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题 目：Some results on weak solutions to the hyperviscous Navier-Stokes equations
时 间：2022.08.22（星期一）10:00-11:00
地点：腾讯会议：869-897-687 会议密码：220822
摘 要：We will talk about our work on weak solutions to the hyperviscous Navier-Stokes equations. This is a joint work with Prof. Peng Qu and Edriss S. Titi.
个人简介：
电子邮箱：twluo@mail.tsinghua.edu.cn
主要工作：主要从事与流体、双曲守恒律相关的非线性偏微分方程的研究，在弱解的适定性、非唯一性等问题做过一系列的工作，比如：可压缩欧拉方程可容许有限值弱解、不可压Navier-Stokes方程分数次耗散弱解的、温度耗散的Boussinesq方程弱解的适定性与不唯一性问题等。
佐证代表性工作的论文信息：
[1.] Luo, Tianwen; Tao, Tao; Zhang, Liqun; Finite energy weak solutions of 2D Boussinesq equations with diffusive temperature, Discrete & Continuous Dynamical Systems, 2020, 40(6), 3737-3765.
[2.] Luo, Tianwen; Qu, Peng; Non-uniqueness of weak solutions to 2D hypoviscous Navier-Stokes equations, Journal of Differential Equations, 2020, 269 (4), 2896-2919.
[3.] Luo, Tianwen; Xie, Chunjing; Titi, Edriss S.; Non-uniqueness of weak solutions to hyperviscous Navier-Stokes equations: on sharpness of J.-L. Lions exponent, Calculus of Variations and Partial Differential Equations, 2020, 59 (3), Paper No. 92, 15 pp.
[4.] Luo, Tianwen; Xie, Chunjing; Xin, Zhouping; Non-uniqueness of admissible weak solutions to compressible Euler systems with source terms, Advances in Mathematics, 2016, 291, 542-583.
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