Xin Zhang (张鑫)

I am currently a tenure-track Associate Professor at School of Mathematical Sciences, Tongji University, Shanghai. Before joining Tongji, I was a postdoctoral researcher in Research Institute for Science and Engineering (理工学術院総合研究所), Waseda University (早稲田大学), working under Prof. Shibata Yoshihiro (柴田 良弘). I obtained my PhD in mathematics in September 2017 from Université Paris-Est Créteil Val-de-Marne, under the supervision of Prof. Danchin Raphaël .

Address

School of Mathematical Sciences, Tongji University,

Siping Road 1239, Shanghai, China (post code: 200092)

Office: Ningjing Building 203

Email: xinzhang2020(at)tongji.edu.cn

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Research interests

Nonlinear partial differential equations in fluid dynamics, free boundary value problem.

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Events

Tongji Seminar on Analysis and PDE

Reading Seminar

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Preprints

• Saito Hirokazu; Zhang, Xin On the dispersive effect of internal gravity waves for the two-phase Stokes semigroup. Submitted.

• Li Ming; Peng Linyu; Zhang Ping; Zhang, Xin Local profiles of self-similar solutions of the planar stationary Navier-Stokes equations. Submitted.

• Fujii Mikihiro; Tsurumi Hiroyuki; Zhang, Xin Decay rates of three dimensional stationary Navier-Stokes flows at the spatial infinity. Submitted.

Published papers

1. Tu Miao; Zhang, Xin On the solution operators arising from the gas-liquid two-phase problem in unbounded domains with finite depth. J. Differential Equations 453 (2026), 113837.

2. Tan, Jin; Tsurumi Hiroyuki; Zhang, Xin On steady solutions of the Hall-MHD system in Besov spaces. Z. Angew. Math. Phys. 76 (2025), no. 4, Paper No. 139.

3. Saito Hirokazu; Xu Jiang; Zhang, Xin; Zhou Wendu On the solvability of weak transmission problem in unbounded domains with non-compact boundaries. J. Math. Fluid Mech. 27 (2025), no. 1, Paper No. 9.

4. Shibata, Yoshihiro; Zhang, Xin Global wellposedness of the 3D compressible Navier-Stokes equations with free surface in the maximal regularity class. Nonlinearity 36 (2023), no. 7, 3710–3733.

5. Shibata, Yoshihiro; Zhang, Xin The Lp-Lq decay estimate for the multidimensional compressible flow with free surface in the exterior domain. J. Differential Equations 325 (2022), 150–205.

6. Saito, Hirokazu; Zhang, Xin Unique solvability of elliptic problems associated with two-phase incompressible flows in unbounded domains. Discrete & Continuous Dynamical Systems-A. 41 (2021), no. 10, 4609-4643.

7. Saito, Hirokazu; Shibata, Yoshihiro; Zhang, Xin Some free boundary problem for two-phase inhomogeneous incompressible flows. SIAM J. Math. Anal. 52 (2020), no. 4, 3397–3443.

8. Zhang, Xin The R-bounded operator families arising from the study of the barotropic compressible flows with free surface. J. Differential Equations 269 (2020), no. 9, 7059–7105.

9. Danchin, Raphaël; Zhang, Xin On the persistence of Hölder regular patches of density for the inhomogeneous Navier-Stokes equations. J. Éc. polytech. Math. 4 (2017), 781–811.

10. Danchin, Raphaël; Zhang, Xin Global persistence of geometrical structures for the Boussinesq equation with no diffusion. Comm. Partial Differential Equations 42 (2017), no. 1, 68–99.

Book

1. Shibata, Yoshihiro; Zhang, Xin Classical solution for the compressible flow with free surface in three dimensional exterior domain. Fluids under control (2023), 241-293, Birkhäuser/Springer.

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Current Teaching

Fall 2026, Real Analysis (graduate course), 64h.

Past Teaching

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Student

Doctoral thesis

Li Ming from September 2026

Xiang Jiaju from September 2026

Master thesis

Wei Zhifan from September 2025

Huang Junye from September 2023, co-advised by Dr. Yang Xiaochuan

Tu Miao, Zhou Wendu (from September 2022) thesis defense on March 14, 2025

Undergraduate