Research interest
My research interest lies in the analysis of Partial differential equations, specifically in the stability and the asymptotic (singular) limits for the systems arising from fluid mechanics and plasma physics.
On one hand, most of my previous work concerns the uniform stability and the singular limits of some fluid systems (Euler or Navier-Stokes type), including the following three types of questions:
1. Low Mach number limit problem for viscous fluid systems in the domain with boundaries. For instance, incompressible limit problem of compressible Navier-Stokes equations in a domain with fixed or free boundaries.
2. Multi-scale limits for non-isentropic viscous fluids in the presence of boundaries.
3. Uniform stability and large time regularity for some systems from plasmas physics (like Navier-Stokes-Poisson) and fluid mechanics (like Euler-Korteweg).
On the other hand, I got interested also in the (in-)stability of some interesting special solutions (like periodic waves, solitons, shear flows...) of some fluid systems (like Euler-Poisson and water waves, compressible Naver-Stokes).
On one hand, most of my previous work concerns the uniform stability and the singular limits of some fluid systems (Euler or Navier-Stokes type), including the following three types of questions:
1. Low Mach number limit problem for viscous fluid systems in the domain with boundaries. For instance, incompressible limit problem of compressible Navier-Stokes equations in a domain with fixed or free boundaries.
2. Multi-scale limits for non-isentropic viscous fluids in the presence of boundaries.
3. Uniform stability and large time regularity for some systems from plasmas physics (like Navier-Stokes-Poisson) and fluid mechanics (like Euler-Korteweg).
On the other hand, I got interested also in the (in-)stability of some interesting special solutions (like periodic waves, solitons, shear flows...) of some fluid systems (like Euler-Poisson and water waves, compressible Naver-Stokes).
Research items
Preprints:
1. Transverse linear stability of one-dimensional solitary gravity water waves.
with F. Rousset, 57 pages, arXiv:2402.11115 (02-2024)
2. Uniform regularity in the low Mach number and inviscid limits for the full Navier-Stokes system in domains with boundaries.
(114 pages, arXiv:2204.09799, accepted by 'Mémoires de la Société Mathématique de France')
(The referee's report provides contextual background and explanations for the results obtained in this study)
Articles:
7. Linear stability of periodic waves for the generalized Korteweg-de Vries equation.
(with C. Audiard, and L.M.Rodrigues), to appear in 'Proceedings of AMS'.
6. Spectral instability of small-amplitude periodic waves of the electronic Euler-Poisson system.
(with P. Noble and L.M. Rodrigues), 'Nonlinearity'. (2023)
5. Incompressible limit for free surface Navier-Stokes equations, with N. Masmoudi and F. Rousset,
93 pages, 'Annals of PDE'. (2023)
4. Uniform estimates for compressible Navier-Stokes equations with low Mach number in bounded domains,
(with N. Masmoudi and F. Rousset).
Journal de Mathématiques Pures et Appliquées.(2022)
3. Long-term regularity of two dimensional Navier-Stokes-Poisson system.
SIAM Journal on Mathematical Analysis. (2021)
2. Stability of equilibria uniformly in the inviscid limit for the Navier-Stokes-Poisson system, with F. Rousset,
Annales de l'Institut Henri Poincare / Analyse non lineaire. (2021)
1. Large time existence of two-fluid Euler-Maxwell and Euler-Korteweg with vorticity.
Nonlinear Anal.(2021)
Thesis manuscript:
Uniform stability for some systems arising from fluid mechanics and plasma physics.
HAL: tel-03462634. (12-2021).
Research funding
1. Starting grants for new researchers, from CNRS.
Date: Feb/2024--, Amount: 20K€.
2. PEPS-JCJC funding for young researchers from INSMI, CNRS ,
Research project: Stability, large time behaviour and singular limit problem in fluid mechanics,
Principle investigator: Changzhen Sun,
Date: Feb-Dec/2022, Amount: 3800€.
Date: Feb/2024--, Amount: 20K€.
2. PEPS-JCJC funding for young researchers from INSMI, CNRS ,
Research project: Stability, large time behaviour and singular limit problem in fluid mechanics,
Principle investigator: Changzhen Sun,
Date: Feb-Dec/2022, Amount: 3800€.
Research activities
Invited talks:
Talks at conferences
- Journées Jeunes EDPistes 2023, Tours, (22-24/03/2023)
- Mathematical Advances in Geophysical Flows, Cirm, (short presentation), 06/04/2022
- Long Time Behavior and Singularity Formation in PDEs, NYU Abu Dhabi, 13(-17)/06/2021,
- Vorticity, Rotation and Symmetry (V)Global Results and Nonlocal Phenomena, Cirm (28/10/2020).
Talks at seminars
- UNIST webnair on nonlinear waves. (24/01/2024)
- Seminar at Shandong university & Lanzhou university. (15/01/2024)
- PDEs seminar at Nanjing university. (12/01/2024)
- Colloquium seminar at CAS. (03/01/2024)
- PDEs seminar at Peking University. (02/01/2024)
- PDEs seminar at CAS, Beijing. (15/11/2023)
- Seminar of analysis of PDEs, LMB, Besançon. (09/11/2023)
- Seminar of PDEs, Poly U, Hong Kong. (18 & 25/09/2023)
- Seminar of SITE center, NYU-Abu-Dhabi. (09/11/2022)
- Seminar on harmonics and PDEs, Chinese Academy of Sciences (CAS). (07/09/2022)
- Seminar of analysis of PDEs, Shandong University (two lectures, 14&18/06/2022)
- Seminar of AGM center, CY Cergy Paris University. (17/01/2022),
- Seminar of PDEs, Peking University. (08/01/2022),
- Seminar on Mathematical physics, Institute of Mathematics of Bordeaux. (16/11/2021),
- Analysis seminar of Beijing Institute of technology. (23/10/2021),
- Seminar on Analysis and Calculation. University Toulouse III, (19/10/2021),
- PDEs seminar, KIT, ( 07/07/2021),
- Seminar on Analysis, Geometry, and PDEs, Lund University. (07/04/2021),
- PDEs seminar of University Rennes 1. (01/04/2021),
- Weekly seminar of PDEs of Chinese young researchers in France. (07/06/2020),
- Seminar of PDEs and numerical analysis, LMO, Orsay. (14/05/2020),
- Student Seminars on PDEs and harmonic analysis, Orsay. (06/02/2020),
- Seminar of PDEs and analysis, Peking University (19/08/2019).
Invited visits
- Peking university, three weeks, invited by Prof. Chao Wang (01/2024)
- University Paris-Sacaly, invited by Prof. Frédéric Rousset (06/2023)
- University of NYU Abu-Dhabi, two weeks, invited by Prof. Nader Masmoudi. (11/2022)
- University of Rennes 1, five weeks, invited by Prof. Miguel Rodrigues. (11/2021&04,07/2022&01,07/2023)
- Institute of Chinese Academy of Sciences, two weeks, invited by Prof Ping Zhang. (07/2019).
Participated Conferences/Summer schools
- When kinetic theory meets fluid mechanics, (ETH, 18-22/07/2022)
- Fluid Mechanics : qualitative study and asymptotic behaviour (Peyresq, 29/08-03/09, 2021)
- Fluid Dynamics : advanced Summer School (Corsica, 13-21/08, 2021)
- 11th Itinerant Workshop in PDEs (HCM, Bonn, 22-24 January, 2020)
- Inhomogeneous flows : Asymptotic models and interface evolution. (Cirm, Marseille, 23-27/09, 2019)
- National graduate summer school on PDEs. (Xiamen, 27/07-11/08, 2019)
- Journées Équations aux Dérivées Partielles (Obernai, 3-8/06, 2019),
- Conference celebrating prof. Jean-Yves-Chemin’s 60th birthday. (IHP, Paris, 25-29/03, 2019).