吕勇 - 南京大学

个人简介

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. Teaching 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.

研究领域

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...

近期论文

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Global solutions of 2D isentropic compressible Navier-Stokes equations with one slow variable(with Ping Zhang) submitted, 56 pages,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 spacesubmitted, 23 pages, arXiv:2003.06821 . 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 .