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About me
About me
From fall semester 2024, I am a Research Assistant Professor (non-tenure track) at the Department of Mathematics of The Chinese University of Hong Kong. Previously, I was a post-doctoral researcher at Laboratoire de Mathématiques AGM, Cergy Paris Université, worked with Prof. Christophe Prange and Prof. Charles Collot. I completed my PhD in Mathematics under the supervision of Prof. Raphaël Danchin and Prof. François Vigneron at Laboratoire d’analyse et de mathématiques appliquées, Université Paris-est Créteil.
Contact information
Contact information
E-mail address: jin.tan@cuhk.edu.hk
Office: 237A, Department of Mathematics, Lady Shaw Building
The Chinese University of Hong Kong
Shatin, N.T., Hong Kong, China
Research interest
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 with variable density, Hall-MHD system. So far, I have conducted research on the following topics:
Symmetry breaking for the Navier-Stokes equations , see [3];
Propagation of free boundary regularity of density patches for viscous inhomogeneous incompressible flows , see [2, 5, 8];
Magnetic relaxation problem, and relaxation limits for compressible fluids, see [1, 4, 6];
Well-posedness for quasilinear parabolic PDEs with low regularity data, see [9, 10, 11, 7].
You can find my PhD thesis and Curriculum Vitae and Orcid link
Preprints and publications
Preprints and publications
[1] Weak solutions of Moffatt’s magnetic relaxation equations,
submitted, arXiv
[2] With C. Prange, Free boundary regularity of vacuum states for incompressible viscous flows in unbounded domains,
submitted, arXiv
[3] With T. Barker and C. Prange, On symmetry breaking for the Navier-Stokes equations,
Communications in Mathematical Physics, 405(25) (2024), Journal link
[4] 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,
Nonlinearity, 37(7)(2024), Journal link
[5] With L. Zhang, Inhomogeneous incompressible Hall-MHD system with only bounded density,
Science China Mathematics (2024), Journal link
[6] 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 link
[7] With F. Vigneron, Global well-posedness and long-time asymptotics of a general nonlinear non-local Burgers equation,
Acta Applicandae Mathematicae, (2024) 192:8, Journal link
[8] Global weak solutions to the density-dependent Hall-magnetohydrodynamics system,
Journal of Mathematical Fluid Mechanics, 23(86) (2021), Journal link
[9] With R. Danchin, The global solvability of the Hall-magnetohydrodynamics system in critical Sobolev spaces,
Communications in Contemporary Mathematics, (2021), Journal link
[10] 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 link
[11] 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 link
Recent talks
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
Support acknowledgement
My research was 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 of CNRS.
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