张鑫 - 同济大学 - 数学科学学院

研究领域

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

近期论文

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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. 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. 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. 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. 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. 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. 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. 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.