Xin Zhang (张鑫)

About

Research

My research focuses on nonlinear partial differential equations in fluid dynamics, free boundary value problems.

Publications

Preprints

1. Saito Hirokazu; Zhang, Xin — On the dispersive effect of internal gravity waves for the two-phase Stokes semigroup. Submitted
2. Li Ming; Peng Linyu; Zhang Ping; Zhang, Xin — Local profiles of self-similar solutions of the planar stationary Navier-Stokes equations. Submitted
3. Fujii Mikihiro; Tsurumi Hiroyuki; Zhang, Xin — Decay rates of three dimensional stationary Navier-Stokes flows at the spatial infinity. Submitted

Journal Articles

1. 10.
   On the solution operators arising from the gas-liquid two-phase problem in unbounded domains with finite depth.

   Tu Miao; Zhang, Xin · J. Differential Equations 453 (2026), 113837
2. 9.
   On steady solutions of the Hall-MHD system in Besov spaces.

   Tan, Jin; Tsurumi Hiroyuki; Zhang, Xin · Z. Angew. Math. Phys. 76 (2025), no. 4, Paper No. 139
3. 8.
   On the solvability of weak transmission problem in unbounded domains with non-compact boundaries.

   Saito Hirokazu; Xu Jiang; Zhang, Xin; Zhou Wendu · J. Math. Fluid Mech. 27 (2025), no. 1, Paper No. 9
4. 7.
   Global wellposedness of the 3D compressible Navier-Stokes equations with free surface in the maximal regularity class.

   Shibata, Yoshihiro; Zhang, Xin · Nonlinearity 36 (2023), no. 7, 3710–3733
5. 6.
   The L^p-L^q decay estimate for the multidimensional compressible flow with free surface in the exterior domain.

   Shibata, Yoshihiro; Zhang, Xin · J. Differential Equations 325 (2022), 150–205
6. 5.
   Unique solvability of elliptic problems associated with two-phase incompressible flows in unbounded domains.

   Saito, Hirokazu; Zhang, Xin · Discrete Contin. Dyn. Syst. 41 (2021), no. 10, 4609–4643
7. 4.
   Some free boundary problem for two-phase inhomogeneous incompressible flows.

   Saito, Hirokazu; Shibata, Yoshihiro; Zhang, Xin · SIAM J. Math. Anal. 52 (2020), no. 4, 3397–3443
8. 3.
   The R-bounded operator families arising from the study of the barotropic compressible flows with free surface.

   Zhang, Xin · J. Differential Equations 269 (2020), no. 9, 7059–7105
9. 2.
   On the persistence of Hölder regular patches of density for the inhomogeneous Navier-Stokes equations.

   Danchin, Raphaël; Zhang, Xin · J. Éc. polytech. Math. 4 (2017), 781–811
10. 1.
    Global persistence of geometrical structures for the Boussinesq equation with no diffusion.

    Danchin, Raphaël; Zhang, Xin · Comm. Partial Differential Equations 42 (2017), no. 1, 68–99

Book Chapters

1. 1.
   Classical solution for the compressible flow with free surface in three dimensional exterior domain.

   Shibata, Yoshihiro; Zhang, Xin · Fluids under control (2023), 241–293, Birkhäuser/Springer

Teaching

Students

Events

• Tongji Seminar on Analysis and PDE
• Reading Seminar