Nanjing University

Department of Mathematics

Yong LU

I am an Associate Professor at Nanjing University.

Research Interests

My research interests lie within the mathematical analysis of partial differential equations.

Mathematical Geometric optics : Stability analysis of WKB solutions; Non-relativistic limit of Klein-Gordon equations...

Mathematical fluid mechanics : Multiple-scale analysis of rotating compressible fluids; Non-Newtonian fluids; Homogenization in fluid mechanics...

Education and Appointment

2006.7: B.S. in Mathematics, University of Science and Technology of China.

2006-2008: Graduate study, Institute of Mathematics, Chinese Academy of Sciences. Supervisor: Ping Zhang.

2009.7: Master in Mathematics, Universite Paris-Diderot (Paris 7). Supervisor: Benjamin Texier.

2013.6: Doctor in Mathematics, Universite Paris-Diderot (Paris 7). Supervisor: Benjamin Texier.

2013.9-2016.9: Postdoctoral Researcher, Mathematical Institute, Charles University in Prague. Mentors: Eduard Feireisl and Josef Malek.

2016.10-2017.11: Associate Researcher, Chern Institute of Mathematics, Nankai University.

2017.12--: Associate Professor, Department of Mathematics, Nanjing University.

Publications and preprints

• Uniform estimates for Stokes equations in domains with small holes and applications in homogenization problems,
  submitted, 26 pages, pdf.
• Homogenization of the compressible Navier-Stokes equations in domains with very tiny holes,
  (with Sebastian Schwarzacher),
  Journal of Differential Equations, Volume 265, Issue 4, 15 August 2018, Pages 1371-1406 ,     pdf.
• Weak-strong uniqueness for the compressible Navier--Stokes equations with a hard-sphere pressure law,
  (with Eduard Feireisl and Antonin Novotny),
  SCIENCE CHINA Mathematics, doi: 10.1007/s11425-017-9272-7 ,     pdf .
• Relative Entropy, Weak-Strong Uniqueness, and Conditional Regularity for a Compressible Oldroyd-B Model,
  (with Zhifei Zhang),
  SIAM Journal on Mathematical Analysis, 50 (2018), no. 1, 557-590 ,     pdf.
• Existence of large-data finite-energy global weak solutions to a compressible Oldroyd-B model,
  (with John W. Barrett and Endre Suli),
  Communications in Mathematical Sciences, Volume 15, Number 5, (2017), 1265-1323 ,     pdf.
• Higher order asymptotic analysis of the nonlinear Klein-Gordon equation in the non-relativistic limit regime,
  (with Zhifei Zhang),
  Asymptotic Analysis, vol. 102, no. 3-4, 2017,157-175,     pdf .
• The inverse of the divergence operator on perforated domains with applications to homogenization problems for the compressible Navier-Stokes system,
  (with Lars Diening and Eduard Feireisl),
  ESAIM: Control, Optimisation and Calculus of Variations, 23 (3) (2017), 851-868. ,     pdf.
• On uniform estimates for Laplace equation in balls with small holes,
  Calculus of Variations and Partial Differential Equations, 55 (5) (2016), 55:110,     pdf.
• Dissipative weak solutions to compressible Navier-Stokes-Fokker-Planck systems with variable viscosity coefficients,
  (with Eduard Feireisl and Endre Suli),
  Journal of Mathematical Analysis and Applications 443(1) (2016) 322-351,     pdf.
• Partially strong transparency conditions and a singular localization method in geometric optics,
  (with Zhifei Zhang),
  Archive for Rational Mechanics and Analysis, 222(1) 2016, 245-283,     pdf.
• On PDE analysis of flows of quasi-incompressible fluids,
  (with Eduard Feireisl and Josef Malek),
  Zeitschrift fur Angewandte Mathematik und Mechanik, 96(4) (2016) 491-508,     pdf.
• Higher-order resonances and instability of high-frequency WKB solutions,
  Journal of Differential Equations, 260(3) (2016) 2296-2353,     pdf.
• Homogenization of stationary Navier-Stokes equations in domains with tiny holes,
  (with Eduard Feireisl),
  Journal of Mathematical Fluid Mechanics, 17(2) (2015), 381-392,     pdf.
• A stability criterion for high-frequency oscillations,
  (with Benjamin Texier),
  Memoires de la Societe Mathematique de France, 142 (2015), vii+130 pp,     pdf.
• Rotating compressible fluids under strong stratification,
  (with Eduard Feireisl and Antonin Novotny),
  Nonlinear Analysis: Real World Applications, 19 (2014) 11-18,     pdf .
• High-frequency limit of the Maxwell-Landau-Lifshitz system in the diffractive optics regime,
  Asymptotic Analysis, 82, no.1-2, (2013), 109-137,     pdf .

Teaching

• Harmonic Analysis , 2017-2018.
  Notice: The course on Tuesday 29th May is canceled.
  Notice: The final exam will be held on 24th June, at the same classroom as the course: Classroom 118.
  


• Analysis II , 2018-2019.
  Notice: The course on Thursday 11th April is canceled.
  Notice: There will be an extra lecture on Saturday 23rd March: 8:00--10:00, Classroom 220.
  Notice: The course on Tuesday 28th May and 4th June are canceled.
  Notice: There will be an extra lecture on Sunday 23rd June: 8:00--12:00, Classroom 208.
  Notice: The final exam will be held on 23th June: 8:00-10:00, at the same classroom as the course: Classroom 208.
  
  



last update: 2018.6

---