TAN Jin

About me

From 2021, I am a post-doctoral researcher at Laboratoire de Mathématiques AGM, Cergy Paris Université. My mentor is Christophe Prange and Charles Collot. Before this position, I completed my PhD in Mathematics under the supervision of Raphaël Danchin and François Vigneron at Laboratoire d’analyse et de mathématiques appliquées, Université Paris-est Créteil.

Contact information

E-mail address: jin.tan@cyu.fr

Office: E533, Département Mathématiques, UMR CNRS 8088

Bâtiment E, cinquième étage

2 Avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France

Research interest

I have a broad interest in the existence, uniqueness and regularity issues for partial differential equations from fluid dynamics and magnetohydrodynamics, such as the Navier-Stokes equations, Hall-MHD system, non-linear non-local equations and so on. Currently, my research focus on the following topics:

Symmetry breaking for the Navier-Stokes equations
Free boundary regularity of density patches for viscous inhomogeneous incompressible flows
Magnetic relaxation problem and singular limits for compressible fluids
Nonlinear stability and rearrangement in hydrodynamics
Self-similar singularity formation

You can find my PhD thesis and Curriculum Vitae, Orcid link

Preprints and publications

Weak solutions of Moffatt’s magnetic relaxation equations,

submitted, arXiv

With C. Prange, Free boundary regularity of vacuum states for incompressible viscous flows in unbounded domains,

submitted, arXiv

With T. Barker and C. Prange, On symmetry breaking for the Navier-Stokes equations,

Communications in Mathematical Physics 405, 25 (2024), Journal

With T.Crin-Barat, Y.-L.Shou, Quantitative derivation of a two-phase porous media system from the one-velocity Baer-Nunziato and Kapila systems,

submitted, arXiv

With L. Zhang, Inhomogeneous incompressible Hall-MHD system with only bounded density,

accepted by Science China Mathematics, hal

With C. Burtea and T. Crin-Barat, Pressure-relaxation limit for a one-velocity Baer–Nunziato model to a Kapila model,

Mathematical Models and Methods in Applied Sciences, 33(04) (2023) 687--753, Journal

With F. Vigneron, Global well-posedness and long-time asymptotics of a general nonlinear non-local Burgers equation,

submitted, arXiv

Global weak solutions to the density-dependent Hall-magnetohydrodynamics system,

Journal of Mathematical Fluid Mechanics, 23(86) (2021), Journal

With R. Danchin, The global solvability of the Hall-magnetohydrodynamics system in critical Sobolev spaces,

Communications in Contemporary Mathematics, (2021), Journal

With L. Liu, Global well-posedness for the Hall-magnetohydrodynamics system in larger critical Besov spaces,

Journal of Differential Equations, 274 (2021) 382--413, Journal

With R. Danchin, On the well-posednessof the Hall-Magnetohydrodynamics system in critical spaces,

Communications in Partial Differential Equations, 46(1) (2021) 31--65, Journal

Recent talks

Seminar, Hunan University, 16 Jan., 2024, Changsha
Seminar, Zhejiang University of Technology, 12 Jan., 2024, Hangzhou
Early Career Math Colloquium, (online) 13 November, 2023
Analyse et EDP, Cergy Paris Université, 14 Nov., 2022, Cergy
Journées Jeunes EDPistes 2022, 23-25 May, 2022, Lyon
PDE seminar of Tongji University, (online) 16 June, 2021, Paris

Support acknowledgement

My current research is partially supported by the Agence Nationale de la Recherche, project BORDS, grant ANR-16-CE40-0027-01 and by the CY Initiative of Excellence, project CYNA (CY Nonlinear Analysis), and by the Labex MME-DII, PEPS JCJC 2023.