This post is a archive of forthcoming seminars led by Prof. Huang's group in 2024 Fall. We will update the relevant informations and upload sources(including recording videos and documents) in this post. Summary The main informations of the topics will be listed here. Please check the last section for the schedule and uploaded sources. Global regularity of compressible flow under sufficiently large density Lecturer: Yongteng Gu(顾永腾) Reference: H. Yu, Global existence of strong solutions to the 3d isentropic compressible navier–stokes equations with density-dependent viscosities, Mathematical Methods in the Applied Sciences, 46 (2023), pp. 10123–10136. Framework of PDE in hydrodynamics Lecturer: Anchun Ni(倪安纯) Global weak solutions of compressible flow with degenerate viscosity Lecturer: Anchun Ni(倪安纯) Reference: Bresch, D., Desjardins, B.: Existence of global weak solutions for 2D viscous shallow water equations and convergence to the quasi-geostrophic model. Commun. Math. Phys. 238(1–3), 211–223 (2003) Mellet,A.,Vasseur, A.:On the barotropic compressible Navier–Stokes equations.Commun. Partial Differ. Equ. 32(1–3), 431–452 (2007) Vasseur A.; Yu C. Existence of global weak solutions for 3D degenerate compressible Navier-Stokes equations. Invent. Math. 206, 935-974 (2016) Global regularity of full Navier-Stokes system under small data Lecturer: Anchun Ni(倪安纯) Reference: X.D. Huang, J. Li, Z.P. Xin, Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations, Commun. Pure Appl. Math. 65(4), 549-585 (2012). X.D. Huang, J. Li, Global classical and weak solutions to the three-dimensional full compressible Navier–Stokes system with vacuum and large oscillations, Arch. Rational Mech. Anal. 227, 995-1059 (2018). Schedule and sources No. Schedule Topic Lecturer Notes Records Location/MeetingID 1 24.08.02 Large density…

This seminar is about the singularity of PDEs in hydrodynamics and quantum mechanics, led by Prof. Huang's group. The relevant informations and sources(including recording videos and documents) will be updated in this post. Contents Our seminar proceed as follows: Ni will mainly introduce the recent works by Merle-Raphaël-Rodnianski-Szeftel, which worked out the Millennium problem in compressible version. Some related topics, like shock waves and other types of singularity, will also considered in our seminar. And Meng and Gu will lecture basic theory of elliptic equations. See references at the end. Schedule and sources We schedule on every Friday, 2:00-5:30 pm, located at Siyuan building S615, AMSS, CAS. No. Schedule Topic Lecturer Notes Records Location 1 24.03.08 Singularity & Stability A. Ni written typed offline S615 2 24.03.08 Laplace's equation 1 Y. Gu typed offline S615 3 24.03.15 Smooth implosion 1 A. Ni written offline S615 4 24.03.15 Moser iteration W. Meng typed offline S615 5 24.03.22 Smooth implosion 2 A. Ni written offline S615 6 24.03.22 Spherical blowup 1 Y. Gu written offline S615 7 24.03.29 Smooth implosion 3 A. Ni written offline S615 8 24.03.29 Perron's method W. Meng written offline S615 9 24.04.05 Smooth implosion 4 A. Ni written offline S615 10 24.04.05 Newtonian Potential W. Meng written offline S615 11 24.04.12 Smooth implosion 5 A. Ni written offline S615 12 24.04.12 Iteration method Y. Gu written offline S615 13 24.04.19 Smooth implosion 6 A. Ni written offline S615 13 24.04.19 Laplace equation 4 W. Meng written offline S615 14 24.04.26 Smooth implosion 7 A. Ni written offline…

This page is a archive of the following seminars led by Prof. Huang's group. We will update the relevant informations and upload sources(including recording videos and documents) in this post. Summary The main informations of the topics will be listed here. Please check the last section for the schedule and uploaded sources. Schauder theory of elliptic equations. Lecturer: Yongteng Gu(顾永腾) Reference: 陈亚浙，二阶椭圆方程与椭圆方程组，科学出版社 (2010). Functional analysis. Lecturer: Weili Meng(孟维利) Reference: H. Brezis, Functional analysis, Sobolev spaces and partial differential equations, Springer (2010). Shock waves and systems of conservation law. Lecturer: Anchun Ni(倪安纯) Reference: T.P. Liu, Shock waves, American Mathematical Society (2021). Remark: We mainly focus on the first four chapter(about convex scalar conservation laws and Burgers equation), the later topics about hyperbolic system will depend on the progress. Global regularity of 2D Kazhihov-Vaigiant model Lecturer: Anchun Ni(倪安纯) Reference: X. D. Huang, J. Li, Existence and blowup behavior of global strong solutions to the two-dimensional barotropic compressible Navier-Stokes system with vacuum and large initial data, J. Math. Pures. Appl. 106(1), 123-154 (2016). V.A. Vaigant, A.V. Kazhikhov, On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscous fluid, Sib. Math. J., 36(6), 1283-1316 (1995). Serrin type blowup criterion of isentropic flow Lecturer: Anchun Ni(倪安纯) Reference: X. D. Huang, J. Li, Serrin-type criterion for the three-dimensional viscous compressible flows, SIAM J. Math. Anal., 43(4), 1872-1886 (2011). Schedule and sources No. Schedule Topic Lecturer Notes Records Location/MeetingID 1 23.11.16 Schauder theory 1 Y. Gu written online 836-1427-6826 2 23.11.17 Functional analysis 1 W. Meng typed online 776-9491-9082 3 23.11.24 Shock waves…

This seminar is mainly about the theory of unbounded operators and its application to the PDEs and dynamic systems. We are scheduled to begin at mid-July, 2023, where lecture sources and meeting videos will be uploaded in this post.

The course is given by Prof. Liu from Peking university in 2023, some lecture notes can be seen on his main page.