Nanjing University

Department of Mathematics

Yong LU

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 : Homogenization in fluid mechanics; Non-Newtonian fluid models...

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 .

2008-2013: Master and 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--2022.12: Associate Professor, Department of Mathematics, Nanjing University.

2023.1--: Professor, Department of Mathematics, Nanjing University.

Publications and preprints

• Unconditional Stability of Equilibria in Thermally Driven Compressible Fluids
  (with Eduard Feireisl and Yongzhong Sun)
  Arch. Ration. Mech. Anal. 248 (2024), no. 6, Paper No. 98. arXiv:2401.01494 .
• Convergence rates in the nonrelativistic limit of the cubic Klein-Gordon equation
  (with Weizhu Bao and Zhifei Zhang)
  SIAM J. Math. Anal. 56 (2024), no. 5, 6822–6860 arXiv:2304.06920 .
• Homogenization of some evolutionary non-Newtonian flows in porous media
  (with Zhengmao Qian)
  J. Differential Equations 411 (2024), 619–639. arXiv:2310.05121 .
• Global solutions of 2D isentropic compressible Navier-Stokes equations with one slow variable
  (with Ping Zhang)
  J. Differential Equations 376 (2023), 406-468.     arXiv:2106.01568 .
• Space-time resonances and high-frequency Raman instabilities in the two-fluid Euler-Maxwell system
  (with Eric Dumas and Benjamin Texier)
  submitted, 133 pages, arXiv:2102.08891 .
• Homogenization of Poisson and Stokes equations in the whole space
  submitted, 23 pages, arXiv:2003.06821 .
• Homogenization of Evolutionary Incompressible Navier-Stokes System in Perforated Domains
  (with Peikang Yang)
  Journal of Mathematical Fluid Mechanics, volume 25, Article number: 4 (2023) ,     arXiv:2204.01207 .
• On planar flows of viscoelastic fluids of Giesekus type
  (with Miroslav Bulicek, Tomas Los, and Josef Malek)
  Nonlinearity 35 (2022) , 6557-6604 .
• Existence, regularity and weak-strong uniqueness for the three-dimensional Peterlin viscoelastic model
  (with Aaron Brunk and Maria Lukacova-Medvidova)
  Communications in Mathematical Sciences, 20 (1) (2022), 201-230 ,     arXiv:2102.02422 .
• On the Cauchy Problem for a Compressible Oldroyd-B Model Without Stress Diffusion,
  (with Sili Liu and Huanyao Wen),
  SIAM J. Math. Anal. 53 (2021), no. 6, 6216-6242 .
• Uniform estimates for Stokes equations in domains with small holes and applications in homogenization problems,
  Calc. Var. Partial Differential Equations 60 (2021), no. 6, Paper No. 228, 31 pp ,     pdf.
• Homogenization of stationary Navier-Stokes-Fourier system in domains with tiny holes,
  (with Milan Pokorny),
  J. Differential Equations 278 (2021), 463-492 ,     pdf.
• Regularity and stability of turbulent solutions for the nonlocal Camassa-Holm equations,
  (with Zaihui Gan and Qing Guo),
  Calc. Var. Partial Differential Equations 60 (2021), no. 1, Paper No. 26, 27 pp ,     pdf.
• Homogenization of a non-homogeneous heat conducting fluid,
  (with Eduard Feireisl and Yongzhong Sun),
  Asymptotic Analysis, vol. 125, no. 3-4, 327-346, 2021 ,     pdf.
• Global existence of large data weak solutions for a simplified compressible Oldroyd-B model without stress diffusion,
  (with Milan Pokorny),
  Anal. Theory Appl. 36 (2020), no. 3, 348-372 ,     pdf.
• Homogenization of Stokes equations in perforated domains: a unified approach,
  J. Math. Fluid Mech. 22 (2020), no. 3, Paper No. 44 ,     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, volume 61, pages 2003-2016 (2018),     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

• Real Analysis, 2023-2024 1st semester.
  
• Real Analysis, 2022-2023, 1st semester.
  
• Linear Algebra, 2021-2022, 1st semester.
  
• Analysis II, 2020-2021, 2nd semester.
  
• Analysis II, 2019-2020, 2nd semester.
  
• Calculus, 2019-2020, 2nd semester.
  
• Linear Algebra, 2019-2020, 1st semester.
  Notice: The courses on Monday 16th September and Wednesday 18th September are moved to Classroom Xian-I-207.
  Notice: The course on Wednesday 25th September is moved to Classroom Xian-II-122.
  
• Analysis II , 2018-2019, 2nd semester.
  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.
  
• Calculus, 2018-2019, 1st semester.
  
• Harmonic Analysis , 2017-2018, 2nd semester.
  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.
  



last update: 2023.12

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