Xin Zhang (张鑫)

Now, I am an assistant professor at School of Mathematical Sciences in Tongji University in Shanghai. Before that, I did my postdoc in Research Institute for Science and Engineering (理工学術院総合研究所) of Waseda University (早稲田大学), with my mentor Prof. Shibata Yoshihiro (柴田 良弘), after my PhD in mathematics in Université Paris-Est Créteil Val-de-Marne under the supervision of Prof. Danchin Raphaël .


School of Mathematical Sciences, Tongji University,
Siping Road 1239, Shanghai, China (post code: 200092)

Office: Ningjing Building 203

Email: xinzhang2020(at)

Research interests

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

ORCID iD icon


Tongji Seminar on Analysis and PDE

Reading Seminar


Published papers

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.


  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.

Current Teaching

Fall 2024, Real Analysis (graduate course, forthcoming), 68h.

Fall 2024, Mordern Theory of Partial Differential Equations (undergraduate course, forthcoming), 51h.

Past Teaching


Master thesis

Li Ming from September 2024

Huang Junye from September 2023

Tu Miao, Zhou Wendu from September 2022


Bian jiahui, Huang Junye, Zhao Yihang June 2023

Tu Miao, Wang Yuange, June 2022