教授（2012年青年破格）、博士生导师、江苏省工业与应用数学学会理事。主要研究方向是非线性偏微分方程，在《Comm. Math. Phys.》、《Arch. Rational Mech. Anal.》、《J. Math. Pures Anal.》、 《SIAM J. Math. Anal.》、《Comm. Part. Diff. Equs.》、《Indiana U. Math. J.》、《J. Diff. Equs.》等国际著名期刊上发表60余篇SCI论文，其中1篇被列为“ESI高被引”论文。主持三项国家自然科学基金项目以及参与一项国家自然科学基金重点项目的研究。曾担任日本九州大学的客座教授和早稻田大学的公派高级研究学者。应邀赴法国、日本、德国、加拿大、香港和澳门的高校或研究所开展学术合作研究。主讲本科生《数学分析》和研究生《泛函分析》等课程，取得了优良的教学效果。2014年入选教育部“新世纪优秀人才支持计划”；2018年荣获南航“良师益友—我最喜爱的导师”；2019年入选南航“长空学者”长空英才；2019年入选教育部“长江学者奖励计划”青年学者；2021年南航“两优一先”表彰中荣获优秀共产党员。

部分研究成果：

S. Kawashima, Y. Shibata and J. Xu, Dissipative structure for symmetric hyperbolic-parabolic systems with Korteweg-type dispersion, Comm. Part. Diff. Equs., 2021, in press.

S. Kawashima, Y. Shibata and J. Xu, The Lp energy methods and decay for the compressible Navier-Stokes equations with capillarity, J. Math. Pures Appl., 154, 146-184, 2021.

Z. Xin and J. Xu, Optimal decay for the compressible Navier-Stokes equations without additional smallness assumptions, J. Differential Equations, 274(15), 543-575, 2021.

H. M. Cao, H. G. Li, C.-J. Xu and J. Xu, The Cauchy problem for the inhomogeneous non-cutoff Kac equation in critical Besov space, J. Differential Equations, 269(2), 1117-1171, 2020.

F. Charve, R. Danchin and J. Xu, Gevrey analyticity and decay for the compressible Navier-Stokes-Korteweg system in the critical framework, Indiana U. Math Journal, 2019, in press.

J. Xu, A low-frequency assumption for optimal time-decay estimates to the compressible Navier-Stokes equations, Comm. Math. Phys., 371, 525-560, 2019.

W. X. Shi and J. Xu, A sharp time-weighted inequality for the compressible  Navier-Stokes-Poisson system in the critical Lp framework, J. Differential Equations, 266(10), 6426-6458, 2019.

R. Danchin and J. Xu, The time-decay estimates for compressible Navier-Stokes equations in the critical Lp framework, Arch. Rational Mech. Anal., 224(1), 53-90, 2017.

J. Xu and S. Kawashima, Frequency-localization Duhamel principle and its application to the optimal decay of dissipative systems, J. Differential Equations, 261, 2670-2701, 2016.

R.-J. Duan, S. Q. Liu and J. Xu, Global well-posedness in spatially critical Besov space for the Boltzmann equation, Arch. Rational Mech. Anal., 220(2),711-745, 2016.

J. Xu, N. Mori and S. Kawashima, Global existence and minimal decay regularity for the Timoshenko system: The case of non-equal wave speeds, J. Differential Equations, 259, 5533-5553, 2015.

J. Xu, N. Mori and S. Kawashima, Lp-Lq-Lr estimates and minimal decay regularity for compressible Euler-Maxwell equations, J. Math. Pures Appl., 104, 965-981, 2015.

J. Xu and S. Kawashima, The optimal decay estimates on the framework of Besov spaces for generally dissipative systems, Arch. Rational Mech. Anal., 218(1), 275-315, 2015.

N. Mori, J. Xu and S. Kawashima. Global existence and optimal decay rates for the Timoshenko system: the case of equal wave speeds, J. Differential Equations, 258(5), 1494-1518, 2015.

J. Xu and S. Kawashima, Global classical solutions for partially dissipative hyperbolic system of balance laws, Arch. Rational Mech. Anal., 211 (2), 513-553, 2014.

J. Xu and S. Kawashima, Diffusive relaxation limit of classical solutions to the damped compressible Euler equations, J. Differential Equations, 256 (2), 771-796, 2014.

Y. J. Peng and J. Xu, Global well-posedness of the hydrodynamic model for two-carrier plasmas, J. Differential Equations, 255(10), 3447-3471, 2013.

J. Xu, J. Xiong and S. Kawashima, Global well-posedness in critical Besov spaces for two-fluid Euler-Maxwell equations, SIAM J. Math. Anal., 45(3), 1422-1447, 2013.

J. Xu and Z. J. Wang, Relaxation limit in Besov spaces for compressible Euler equations, J. Math. Pures Appl., 99(1), 43-61, 2013.

J. Xu, Energy-transport and drift-diffusion limits of nonisentropic Euler-Poisson equations, J. Differential Equations, 252(2), 915-940, 2012.

J. Xu, Global classical solutions to the compressible Euler-Maxwell equations, SIAM J. Math. Anal., 43(6), 2688-2718, 2011.

J. Xu and Wen-A.Yong, Relaxation-time limits of non-isentropic hydrodynamic models for semiconductors, J. Differential Equations, 247(6), 1777-1795, 2009.

J. Xu, Relaxation-time limit in the isothermal hydrodynamic model for semiconductors, SIAM J. Math. Anal., 40(5), 1979-1991, 2008.

人才培养：自2009年9月起，指导了14位硕士生，9位博士生，1位加纳籍留学博士生。