International Conference on Recent Advances in Fluid Dynamics and Nonlinear Dynamics June 2–June 5, 2019 Sichuan University, Chengdu, China Conference on “Recent Advances in Fluid Dynamics and Nonlinear Dynamics” College of Mathematics, Sichuan University, Chengdu, China June 2-5, 2019 Objectives The aim of this international conference is to bring together experts who works on diverse frontiers of nonlinear PDEs and their appli- cations to survey recent progress and current challenges, to discuss how new ideas and methods could advance the related fields in com- ing years. The conference will contribute in promoting, enhancing, and stimulating cross-continental research interactions and collabo- rations in advanced mathematics applied to nonlinear sciences. Organizing Committee Co-Chairs Tian Ma (Sichuan University) Shouhong Wang (Indiana University, USA) Secretary Quan Wang (Sichuan University) Members Daozhi Han (Missouri University of Science and Technology) Hong Luo (Sichuan Normal University) Limei Li (Sichuan Normal University) Ruikuan Liu (Southwest Petroleum University) Zhigang Pan (Southwest Jiaotong University) Sponsorship College of Mathematics, Sichuan University 1 Conference Logistics 1. Registration: 1:00pm-11:00pm, June 2, 2019. 2. Time and Venue: • Invited talks, June 3-4, 2019. • Free discussions, June 5, 2019. • Conference Hall 303, College of Mathematics Building, Sichuan Uni- versity. 3. Accommodation: Kehua Hotel, No.141 Kehua North Road,Wuhou Dis- trict, Chengdu, China. 4. Meals: All meals are provided at Kehua Hotel. 5. Transport Information: • From Shuangliu International Airport to Kehua Hotel: 50RMB by taxi. • From Chengdu East Train Station to Kehua Hotel: 30RMB by taxi. • From Chengdu North Railway Station to Kehua Hotel: 50RMB by taxi. • From Kehua Hotel to Conference Hall 303: 10 minutes walk. 6. Pick-Up Service: We offer pick-up service, please send to Quan Wang (Email: [email protected]) your flight details before May 28, 2019. 7. Contact: Quan Wang, Phone +8613558629124. 8. Registration Fee: There will be no conference fee for this meeting. College of Mathematics, Sichuan University May 22, 2019 2 The Route from Hotel to Meeting place List of Invited Speakers 1. Dongho Chae (Chung-Ang University) Email: [email protected] 2. Daozhi Han (Missouri University of Science and Technology) Email: [email protected] 3. Chun-Hsiang Hsia (National Taiwan University) Email: [email protected] 4. Song Jiang (Institute of Applied Physics and Computational Mathemat- ics, Beijing) Email: [email protected] 5. Boualem Khouider (University of Victoria) Email: [email protected] 6. Chanh Kieu (Indiana University Bloomington) Email: [email protected] 7. Limei Li (Sichuan Normal University) Email: [email protected] 8. Honghu Liu (Virginia Tech) Email: [email protected] 9. Ruikuan Liu (Southwest Petroleum University) Email: [email protected] 10. Anna L. Mazzucato (Penn State University) Email: [email protected] 11. Ruyun Ma (Xidian University) Email: [email protected] 12. Tian Ma (Sichuan University) Email: [email protected] 13. Taylan Sengul (Marmara University) Email: [email protected] 14. Chunyou Sun (Lanzhou University ) Email: [email protected] 15. Jianwen Sun (Lanzhou University ) Email: [email protected] 3 16. Quan Wang (Sichuan University) Email: [email protected] 17. Shouhong Wang (Indiana University Bloomington) Email: [email protected] 18. Xiaoming Wang (Southern University of Sciences and Technology) Email: [email protected] 19. Yongfu Wang (Southwestern University of Finance and Economics) Email: [email protected] 20. Yao Xu (Nanjing University) Email: [email protected] 21. Peihao Zhao (Lanzhou University) Email: [email protected] 4 Schedule for Invited Lectures 5 June 3, 2019 9:00am–9:10am Opening Ceremony 9:10am–9:20am Group Photo Chair: Shouhong Wang (Indiana University, USA) Song Jiang (Institute of Applied Physics and Com- putational Mathematics, Beijing, China) 9:20am–9:50am Magnetic inhibition effect on the Rayleigh-Taylor in- stability in non-resistive magnetohydrodynamics Honghu Liu (Virginia Tech, USA) 9:50am–10:20am A variational approach to closure of nonlinear dynam- ical systems based on small-scale parameterizations 10:20am–10:40am Tea Break Chair: Dongho Chae (Chung-Ang University, Korea) Chanh Kieu (Indiana University, USA) 10:40am–11:10am On the application of the dynamical transition to the tropical cyclone formation problem Quan Wang (Sichuan University, China) Dynamic transitions in axisymmetric nonlinear sys- 11:10am–11:40am tems and application to a two-layer quasi-geostrophic model in an annular channel 12:00pm–1:00pm Lunch Time 6 June 3, 2019 Chair: Song Jiang (Institute of Applied Physics and Computational Math- ematics, Beijing, China) Anna Mazzucato (Penn State University, USA) 2:30pm–3:00pm Boundary layers and the vanishing viscosity limit for incompressible flows Chunyou Sun (Lanzhou University, Guangzhou Uni- 3:00pm–3:30pm versity, China) Inertial manifolds for the 3D modified-Leray-model Limei Li (Sichuan Normal University, China) 3:30pm–4:00pm L2-asymptotic stability of mild solutions to Magneto- hydrodynamic Benard-Convection system 4:00pm–4:20pm Tea Break Chair: Dun Zhao (Lanzhou University) Ruyun Ma (Xidian University, China) 4:20pm–4:50pm Global structure of radial positive solutions for a pre- scribed mean curvature problem Taylan Sengul (Marmara University, Turkey) 4:50pm–5:20pm Stability and Transitions of Quasi-Geostrophic Equa- tions Yao Xu (Nanjing University, China) 5:20pm–5:50pm Homogenization of Elliptic Systems with Stratified Structure 6:20pm–7:20pm Dinner Time 7 June 4, 2019 Chair: Ruyun Ma (Xidian University, China) Dongho Chae (Chung-Ang University, Korea) 9:00am–9:30am On the Type I blow-up for the incompressible Euler equations Tian Ma1 and Shouhong Wang2 (Sichuan Univer- sity1, Indiana University2) 9:30am–10:00am Field Theoretical Interpretation of Quantum Mechan- ical Wave Functions and the Mechanism of High Tc Superconductivity Peihao Zhao (Lanzhou University, China) 10:00am–10:30am Some regularity results in Musielak-Orlicz-Sobolev spaces 10:30am–10:50am Tea Break Chair: Jianxun Hu (Sun Yat-Sen University, China) Boualem Khouider (University of Victoria, Canada) 10:50am–11:20am Towards a Stochastic Relaxation for the Quasi- Equilibrium Theory of Cumulus Parameterization: Multicloud Instability, Multiple Equilibria and Chaotic Dynamics Yongfu Wang (Southwestern University of Finance and Economics, China) 11:20am–11:50am Steady collision of two jets issuing from two axially symmetric channels 12:20pm–1:30pm Lunch Time 8 June 4, 2019 Chair: Peihao Zhao (Lanzhou University, China) Daozhi Han (Missouri University of Science and Technology, USA) 2:30pm–3:00pm On the design of super-convergent, unconditionally stable and solvable numerical schemes for the Cahn- Hilliard fluid models Jianwen Sun (Lanzhou University, China) 3:00pm–3:30pm Some Nonlocal Dispersal Equations and Applications Ruikuan Liu (Southwest Petroleum University, 3:30pm–4:00pm China) Magneto-hydrodynamical Model for Plasma 4:00pm–4:20pm Tea Break Chair: Tianqing An (Hohai University, China) Chun-Hsiung Hsia (National Taiwan University) On the mathematical analysis of the synchronization 4:20pm–4:50pm theory with time-delayed effect Xiaoming Wang (Southern University of Sciences 4:50pm–5:20pm and Technology, China) Coupling and decoupling of free flow and porous media flow 6:00pm–7:00pm Dinner Time 9 June 5, 2019 Free Discussions 10 Abstracts of Invited Talks On the Type I blow-up for the incompressible Euler equations Dongho Chae Chung-Ang University, Korea Email: [email protected] In this talk we discuss the Type I blow up and the related problems in the 3D Euler equa- tions. We say a solution v to the Euler equations satisfies Type I condition at possible blow − kr k 1 1 up time T∗ if lim supt%T∗ (T∗ t) v(t) L < + . The scenario of Type I blow up is a natural generalization of the self-similar(or discretely self-similar) blow up. We present some recent progresses of our study regarding this. We first localize previous result that “small Type I blow up” is absent. After that we show that the atomic concentration of energy is excluded under the Type I condition. This result, in particular, solves the problem of re- moving discretely self-similar blow up in the energy conserving scale, since one point energy concentration is necessarily accompanied with such blow up. We also localize the Beale-Kato- Majda type blow up criterion. Using similar local blow up criterion for the 2D Boussinesq equations, we can show that Type I and some of Type II blow up in a region off the axis can be excluded in the axisymmetric Euler equations. These are joint works with J. Wolf. On the design of super-convergent, unconditionally stable and solvable numerical schemes for the Cahn-Hilliard fluid models Daozhi Han Missouri University of Science and Technology Email: [email protected] The Cahn-Hilliard fluid systems, such as the Cahn-Hilliard-Navier-Stokes equations andthe Cahn-Hilliard-Darcy equations, are popular diffuse interface models for multiphase moving boundary problems. These systems are difficult to solve due to the stiffness associated with the diffusive interface, the high-order nonlinear nature of the PDE systems, andthemo- tion of the relatively sharp front in advection-dominated regime in many applications. In this talk, we discuss the design of super-convergent, unconditionally stable and uniquely solvable numerical schemes for solving Cahn-Hilliard fluid models. The main ideas