Personal Profile
Dr Xu Lingda graduated from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, under the supervision of Research Fellow Huang Feimin. He subsequently undertook postdoctoral research at Tsinghua University and The Hong Kong Polytechnic University, working under the joint supervision of Professor Yu Pin and Professor Yang Tong. His primary research focus lies in the study of nonlinear partial differential equations.
Research Interests
Fluid dynamics and kinematics equations, shock wave formation theory, fluid transition threshold theory.
Educational Background
PhD / 2015–2020 University of Chinese Academy of Sciences Applied Mathematics (Partial Differential Equations)
Bachelor's Degree / 2011–2015 Xiamen University Mathematics and Applied Mathematics
Work Experience
2023-2025 The Hong Kong Polytechnic University Postdoctoral Researcher
2020-2023 Tsinghua University Postdoctoral Fellow
Honours and Awards
September 2023: Nominated for the Fifth China Youth PDE Forum Outstanding Paper Award; Tsinghua University Outstanding Benefactor Scholar
March 2014: First Prize, National Undergraduate Mathematics Competition (12th place)
November 2013: First Prize, Fifth National Undergraduate Mathematics Competition (Preliminary Round) (1st place)
November 2019: National Scholarship for Doctoral Candidates
2012–2015: Selected for the Outstanding Undergraduate Cultivation Programme and awarded multiple scholarships
Publications
[1] Feimin Huang, Lingda Xu and Qian Yuan, Asymptotic stability of planar rarefaction waves under periodic perturbations for 3-d Navier-Stokes equations, Adv. Math. 404 (2022), Paper No. 108452.
[2] Feimin Huang and Lingda Xu, Decay rate toward the traveling wave for scalar viscous conservation law, Commun. Math. Anal. Appl., 1 (2022), pp. 395-409.
[3] Lingjun Liu, Danli Wang and Lingda Xu, Asymptotic stability of the combination of a viscous contact wave with two rarefaction waves for 1-D Navier-Stokes equations under periodic perturbations. J. Differ. Equations., 346, 254-276 (2023).
[4] Meichen Hou, Lingjun Liu, Shu Wang and Lingda Xu, Vanishing viscosity limit to the planar rarefaction wave with vacuum for 3-D full compressible Navier-Stokes equations with temperature-dependent transport coefficients. Math. Ann. Volume 390, pages 3513–3566, (2024)
[5] Feimin Huang and Lingda Xu, Decay rate toward the planar rarefaction wave for scalar viscous conser vation law in several dimensions. Commun. Math. Res., to appear.
[6] Lingjun Liu, Guiqin Qiu, Shu Wang, Lingda Xu, Optimal decay rate to the contact discontinuity for Navier–Stokes equations under generic perturbations. Appl. Math. Lett. 163(2025). , Paper No. 109461, 6 pp.
[7] Lin Chang, Lingjun Liu and Lingda Xu, Nonlinear stability of planar shock wave to 3-D compressible Navier-Stokes equations in half space with Navier Boundary conditions. (Nonlinreaity, 2025.)
[8] Guiqin Qiu and Lingda Xu, Zero dissipation and time decay rates to the planar rarefaction wave for 3-D compressible Euler equation in the whole space. ( Journal of Differential Equations，2025)
[9] Fei Wang, Lingda Xu and Zeren Zhang,The stability threshold for 3D MHD equations around Couette with rationally aligned magnetic field. ( SIAM. JMA., Accepted)