My research interest lies in the mathematical analysis of fluid mechanics.
Publications
[1] 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. doi.org/10.1080/03605302.2016.1252394
[2] 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. jep.cedram.org/jep-bin/fitem?id=JEP_2017__4__781_0
[3] Xin Zhang The R−bounded operator families arising from the study of the barotropic compressible flows with free surface
Journal of Differential Equations 269 (2020), no. 9, 7059-7105. doi: 10.1016/j.jde.2020.05.017
[4] Hirokazu Saito, Yoshihiro Shibata, Xin Zhang Some free boundary problem for two-phase inhomogeneous incompressible flows
SIAM J. Math. Anal. 52 (2020), no. 4, 3397–3443. doi:10.1137/18M1225239
Preprint
[5] Hirokazu Saito, Xin Zhang Unique solvability of elliptic problems associated with two-phase incompressible flows in unbounded domains
submitted, (2019) arxiv.org/abs/1912.00135
[6] Yoshihiro Shibata, Xin Zhang The Lp-Lq decay estimate for the multidimensional compressible flow with free surface in the exterior domain
submitted, (2021)