 Yong LU

Department of Mathematics
Nanjing University
22 Hankou Road, Gulou District
210093, Nanjing
ChinaEmail: luyong(at)nju.edu.cn
Professor at Nanjing University.
Research Interests
My research interests lie within the mathematical analysis of partial differential equations.
Education and Appointment
Publications and preprints
 Convergence rates in the nonrelativistic limit of the cubic KleinGordon equation
(with Weizhu Bao and Zhifei Zhang)
submitted, 38 pages, arXiv:2304.06920 .  Global solutions of 2D isentropic compressible NavierStokes equations with one slow variable
(with Ping Zhang)
J. Differential Equations 376 (2023), 406468. arXiv:2106.01568 .  Spacetime resonances and highfrequency Raman instabilities in the twofluid EulerMaxwell 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 NavierStokes 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) , 65576604 .  Existence, regularity and weakstrong uniqueness for the threedimensional Peterlin viscoelastic model
(with Aaron Brunk and Maria LukacovaMedvidova)
Communications in Mathematical Sciences, 20 (1) (2022), 201230 , arXiv:2102.02422 .  On the Cauchy Problem for a Compressible OldroydB Model Without Stress Diffusion,
(with Sili Liu and Huanyao Wen),
SIAM J. Math. Anal. 53 (2021), no. 6, 62166242 .  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 NavierStokesFourier system in domains with tiny holes,
(with Milan Pokorny),
J. Differential Equations 278 (2021), 463492 , pdf.  Regularity and stability of turbulent solutions for the nonlocal CamassaHolm 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 nonhomogeneous heat conducting fluid,
(with Eduard Feireisl and Yongzhong Sun),
Asymptotic Analysis, vol. 125, no. 34, 327346, 2021 , pdf.  Global existence of large data weak solutions for a simplified compressible OldroydB model without stress diffusion,
(with Milan Pokorny),
Anal. Theory Appl. 36 (2020), no. 3, 348372 , 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 NavierStokes equations in domains with very tiny holes,
(with Sebastian Schwarzacher),
Journal of Differential Equations, Volume 265, Issue 4, 15 August 2018, Pages 13711406 , pdf.  Weakstrong uniqueness for the compressible NavierStokes equations with a hardsphere pressure law,
(with Eduard Feireisl and Antonin Novotny),
Science China Mathematics, volume 61, pages 20032016 (2018), pdf .  Relative Entropy, WeakStrong Uniqueness, and Conditional Regularity for a Compressible OldroydB Model,
(with Zhifei Zhang),
SIAM Journal on Mathematical Analysis, 50 (2018), no. 1, 557590 , pdf.  Existence of largedata finiteenergy global weak solutions to a compressible OldroydB model,
(with John W. Barrett and Endre Suli),
Communications in Mathematical Sciences, Volume 15, Number 5, (2017), 12651323 , pdf.  Higher order asymptotic analysis of the nonlinear KleinGordon equation in the nonrelativistic limit regime,
(with Zhifei Zhang),
Asymptotic Analysis, vol. 102, no. 34, 2017,157175, pdf .  The inverse of the divergence operator on perforated domains with
applications to homogenization problems for the compressible
NavierStokes system,
(with Lars Diening and Eduard Feireisl),
ESAIM: Control, Optimisation and Calculus of Variations, 23 (3) (2017), 851868. , 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 NavierStokesFokkerPlanck systems with variable viscosity coefficients,
(with Eduard Feireisl and Endre Suli),
Journal of Mathematical Analysis and Applications 443(1) (2016) 322351, 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, 245283, pdf.  On PDE analysis of flows of quasiincompressible fluids,
(with Eduard Feireisl and Josef Malek),
Zeitschrift fur Angewandte Mathematik und Mechanik, 96(4) (2016) 491508, pdf.  Higherorder resonances and instability of highfrequency WKB solutions,
Journal of Differential Equations, 260(3) (2016) 22962353, pdf.  Homogenization of stationary NavierStokes equations in domains with tiny holes,
(with Eduard Feireisl),
Journal of Mathematical Fluid Mechanics, 17(2) (2015), 381392, pdf.  A stability criterion for highfrequency 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) 1118, pdf .  Highfrequency limit of the MaxwellLandauLifshitz system in the diffractive optics regime,
Asymptotic Analysis, 82, no.12, (2013), 109137, pdf . 
Real Analysis, 20232024 1st semester.

Real Analysis, 20222023, 1st semester.

Linear Algebra, 20212022, 1st semester.

Analysis II, 20202021, 2nd semester.

Analysis II, 20192020, 2nd semester.

Calculus, 20192020, 2nd semester.

Linear Algebra, 20192020, 1st semester.
Notice: The courses on Monday 16th September and Wednesday 18th September are moved to Classroom XianI207.
Notice: The course on Wednesday 25th September is moved to Classroom XianII122.

Analysis II , 20182019, 2nd semester.
Notice: The course on Thursday 11th April is canceled.
Notice: There will be an extra lecture on Saturday 23rd March: 8:0010:00, 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: 8:0012:00, Classroom 208.
Notice: The final exam will be held on 23th June: 8:0010:00, at the same classroom as the course: Classroom 208.

Calculus, 20182019, 1st semester.

Harmonic Analysis , 20172018, 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.
Teaching
last update: 2023.12