I am Quoc Hung Nguyen.  I am currently an Associate Professor at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences (CAS), Beijing, China. I obtained my Ph.D. in Mathematics from Laboratoire de Mathématiques et Physique Théorique, Université de Tours, France in 2014.  

Here is my website: https://nguyenquochung1241.wixsite.com/qhung

​My research interests: Partial Differential Equations and Analysis.

Submitted papers:

 50) Ke Chen, Ruilin Hu, Quoc-Hung Nguyen, {\em Local well-posedness of the $1d$ compressible Navier-Stokes system with rough data}, arXiv:2206.14160

   49)   Lingjia Huang, Quoc-Hung Nguyen and Yiran Xu, {\em Nonlinear Landau damping for the 2d Vlasov-Poisson system with massless electrons around Penrose-stable equilibria}, arXiv:2206.11744

  48) Nhan-Phu Chung, Quoc-Hung Nguyen, {\em Gradient flows of modified Wasserstein distances and porous medium equations with nonlocal pressure}, arXiv:2205.08748

  47)  Quoc-Hung Nguyen, Nguyen Cong Phuc, {\em Comparison estimate for singular

  $p$-Laplace equation and its consequences}, arXiv:2202.11318

  46)  Lingjia Huang, Quoc-Hung Nguyen and Yiran Xu,  {\em Sharp estimates for screened Vlasov-Poisson system around Penrose-stable equilibria in $\mathbb{R}^d $, $ d\geq3$},arXiv:2205.10261.

 45)   Quoc Anh Ngo, Quoc-Hung Nguyen, and  Van Hoang  Nguyen,  {\em An optimal Hardy-Littlewood-Sobolev inequality on $\mathbf{R}^{n-k}\times\mathbf{R}^{n}$  and its consequences },  submitted, arXiv:2009.09868.

 44) Ke Chen  and Quoc-Hung Nguyen, {\em The Peskin Problem with $B^1_{\infty,\infty}$ initial data}, submitted,arXiv:2107.13854.

 43) Ke Chen,  Quoc-Hung Nguyen and Na Zhao, {\em Global  Calder\'{o}n--Zygmund theory for parabolic $p$-Laplacian system: the case $1<p\leq \frac{2n}{n+2}$,} submitted, arXiv:2109.02595.

Published/Accepted Papers:

42) Quoc-Hung Nguyen, Yannick Sire, Le Xuan Truong; {\em Hölder continuity of solutions for a class of drift-diffusion equations}, Discrete and Continuous Dynamical Systems, \href{https://arxiv.org/abs/2003.10848}{arXiv:2003.10848 }

   41) Quoc-Hung Nguyen, Matthew Rosenzweig and Sylvia Serfaty, {\em Mean-field limits of Riesz-type singular flows with possible transport noise}, Ars Inveniendi Analytica (2022), Paper No. 4, 45 pp, DOI: https://doi.org/10.15781/nvv7-jy87\href{https://arxiv.org/abs/2107.02592}{arXiv:2107.02592.}

  40)   Thomas Alazar,  Quoc-Hung Nguyen,  {\em Endpoint Sobolev theory for the Muskat equation}, Communications in Mathematical Physics (to appear) \href{https://arxiv.org/abs/2010.06915}{arXiv:2010.06915.}

 39)   Thomas Alazar,  Quoc-Hung Nguyen, {\em Quasilinearization of the 3D Muskat equation, and applications to the critical Cauchy problem},  Advances in Math ( to appear), arXiv:2103.02474.

 38)   Ke Chen, Quoc-Hung Nguyen, and  Yiran Xu,  {\em The Muskat problem with $C^1$ data},  Trans. AMS ( to appear),  arXiv:2103.09732.

 37) Thomas Alazard, Omar Lazar and Quoc-Hung Nguyen,  {\em On the dynamics of the roots of polynomials under differentiation},  Journal de mathematiques pures et appliqu\'ees ( to appear), 162,1-22, 2022,\\ https://doi.org/10.1016/j.matpur.2022.04.001,

 36) Quoc-Hung Nguyen; {\em Potential estimates and quasilinear parabolic equations with measure data,} Memoirs of the AMS, (2021), to appear, 120 pages. (\href{https://arxiv.org/submit/3703478}{3703478}).

 35) Quoc-Hung Nguyen   {\em Quantitative estimates for regular Lagrangian flows with BV vector fields,} (2021) Comm. Pure Appl. Math., 74: 1129-1192.\\ https://doi.org/10.1002/cpa.21992

 34) Quoc-Hung Nguyen, Nguyen Cong Phuc; {\em Existence and regularity estimates for quasilinear equations with measure data: the case $1<p\leq \frac{3n-2}{2n-1}$}, Analysis and PDEs (2021) (to appear), arXiv:2003.03725v1.

 33)  E. Brué, Quoc-Hung Nguyen:  {\em Advection diffusion equations with Sobolev velocity field,} Commun. Math. Phys. 383, 465–487 (2021),\\ https://doi.org/10.1007/s00220-021-03993-4

32)  Hoai-Minh Nguyen, Quoc-Hung Nguyen, {\em The Weyl law of transmission eigenvalues and the completeness  of generalized transmission eigenfunctions} Journal of Functional Analysis,

 Volume 281, Issue 8, 2021,109146.

 31) Thomas Alazar,   Quoc-Hung Nguyen, {\em On the Cauchy problem for the Muskat equation with non-Lipschitz initial data}, Communications in Partial Differential Equations, 2021 DOI: 10.1080/03605302.2021.1928700.

 30)   Thomas Alazar,   Quoc-Hung Nguyen,  {\em On the Cauchy problem for the Muskat equation. II: Critical initial data}, Ann. PDE, 7, 7 (2021).\\ https://doi.org/10.1007/s40818-021-00099-x. 

 29)  Quoc-Hung Nguyen,  Yannick sire, Juan-Luis V\'azquez; {\em  A simple proof of the generalized Leibniz rule on bounded Euclidean domains}, Forum Mathematicum,  2021, pp. 000010151520200228. https://doi.org/10.1515/forum-2020-0228

 28)  Le Trong Thanh Bui,  Quoc-Hung Nguyen; {\em Gradient weighted norm inequalities for very weak solutions of linear parabolic equations with BMO coefficients}, Asymptotic Analysis (2021) 1–15, DOI 10.3233/ASY-211693.

 27)  Quoc-Hung Nguyen, Nguyen Cong Phuc; {\em Quasilinear Riccati type equations with oscillatory and singular data}, Advanced Nonlinear Studies (2020) Volume 20, Issue 2, Pages 373–384 ,https://doi.org/10.1515/ans-2020-2079.

 26)  E. Brué, Quoc-Hung Nguyen:  {\em Sobolev estimates for solutions of the transport equation and ODE flows associated to non-Lipschitz drifts,} Math. Ann. (2020). https://doi.org/10.1007/s00208-020-01988-5

 25)  M.F. Bidaut-Veron, Quoc-Hung Nguyen, L. Veron; {\em Quasilinear elliptic equations with a source reaction term involving the function and its gradient and measure data,} Calculus of Variations and Partial Differential Equations  59,  148 (2020).

 24)  Nguyen-Anh Dao, Jesus Ildefonso Diaz,  Quoc-Hung Nguyen, {\em Fractional Sobolev inequalities revisited: the maximal function approach,}  Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. Volume 31, Issue 1, 2020, pp. 225–236DOI: 10.4171/RLM/887

 23) E. Brué, Quoc-Hung Nguyen: {\em Sharp regularity estimates for solutions to the continuity equation drifted by Sobolev vector fields}, Analysis and PDEs (2020), to appear, arXiv:1806.03466v2.

 22) E. Brué, Quoc-Hung Nguyen:  {\em On the Sobolev space of functions with derivative of logarithmic order,} Adv. Nonlinear Anal. 2020; 9: 836–849.

 21) Quoc-Hung Nguyen, Nguyen Cong Phuc; {\em Pointwise estimate for gradient of solutions to quasilinear problem in singular case},Journal functional analysis, (2020), {\bf  278} 108391.

 20)  Quoc-Hung Nguyen, Phuoc-Tai Nguyen, Bao Quoc Tang {\em Energy conservation for inhomogeneous incompressible and compressible Euler equations}, Journal of Differential Equations, Volume 269, Issue 9, 15 October 2020, Pages 7171-7210.

 19)  M.F. Bidaut-Veron, Quoc-Hung Nguyen, L. Veron; {\em Quasilinear and Hessian Lane-Emden Type Systems with Measure Data,}  Potential Analysis, volume 52, pages 615–643(2020).

 18)  Quoc-Hung Nguyen, Phuoc-Tai Nguyen, Bao Quoc Tang {\em Energy equalities for compressible Navier-Stokes equations},  Nonlinearity, (2019), {\bf  23}.

 17) E. Brué, Quoc-Hung Nguyen, Giorgio Stefani: {\em A maximal functiona characterization of absolutely continouos measures and sobolev functions}, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., (2019), {\bf  30} 599–614.

 16)   Quoc-Hung Nguyen, Phuoc-Tai Nguyen; {\em Onsager's conjecture on the energy convervation for solutions of Euler's equation in bounded domains}, Journal of nonlinear science, (2018), {\bf  29} 207–213.

 15)  Quoc-Hung Nguyen, Nguyen Cong Phuc; {\em Good-$\lambda$  and Muckenhoupt-Wheeden type bounds in quasilinear measure datum problems, with applications}, Mathematische Annalen,  (2018), 1–32.

 14) Nguyen-Anh Dao, Jesus Ildefonso Diaz,  Quoc-Hung Nguyen, {\em  Generalized Gagliardo-Nirenberg  inequalities using Lorentz spaces and BMO}, Nonlinear Analysis: Theory, Methods, Applications., (2018), {\bf  173} 146-153.

 13)  Nguyen-Anh Dao, Quoc-Hung Nguyen {\em Brezis-Gallouet-Wainger type inequality with critical  fractional Sobolev space and BMO,}  Comptes Rendus Mathematique, (2018), {\bf  356} 747-756.

 12)  Quoc-Hung Nguyen, Juan Luis V\'azquez; {\em  Porous medium equation with nonlocal pressure in a bounded domain,}  Communications in Partial Differential Equations, (2017), {\bf  43} 1502-1539.

 11)  Hoai-Minh Nguyen, Quoc-Hung Nguyen; {\em Discreteness of interior transmission eigenvalues revisited,} Calculus of Variations and Partial Differential Equations,  (2017) 56: 51. doi:10.1007/s00526-017-1143-7.

 10) Nguyen-Anh Dao, Quoc-Hung Nguyen; {\em Nonstationary Navier-Stokes equations with singular time-dependent external forces,} Comptes Rendus Mathematique,  (2017), {\bf  355}, 966-972.

 9)   M. F. Bidaut-V\'eron, Quoc-Hung Nguyen; {\em Pointwise estimates and existence of solutions of porous medium and $p$-Laplace evolution equations with absorption and measure data,} 

di Scienze  Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) {\bf16} (2016), no. 2, 675-705. 8)  Quoc-Hung Nguyen, L. V\'eron; {\em Wiener criteria for existence of large solutions of nonlinear parabolic equations with absorption in a non-cylindrical domain,} Journal of Differential Equations,  {\bf  260},  4805–4844 (2016).

 7) M.F. Bidaut-Veron, Giang Hoang, Quoc-Hung Nguyen, L. Veron; {\em An elliptic semilinear equation with source term and boundary measure data}, Journal of Functional Analysis, {\bf  269},  1995–2017 (2015).

 6)  Quoc-Hung Nguyen; {\em Global estimates for quasilinear parabolic equations on Reifenberg flat domains and its applications to  Riccati type parabolic equations with distributional data}, Calculus of Variations and Partial Differential Equations, {\bf  54},  3927-3948 (2015).

 5) M. F. Bidaut-V\'eron, Quoc-Hung Nguyen; {\em Evolution equations of $p$-Laplace type with absorption or source terms and measure data,} Communications in Contemporary Mathematics,  {\bf17}, 1550006, (2015).

 4)  M. F. Bidaut-V\'eron, Quoc-Hung Nguyen; {\em Stability properties for quasilinear parabolic equations with measure data,} ~Journal of the European Mathematical Society , {\bf  17},  2103–2135 (2015).

3)  Quoc-Hung Nguyen, L. V\'eron; {\em Wiener criteria for existence of large solutions of quasilinear elliptic equations with absorption,} Potential Analysis, 42,  681-697 (2015).

 2)  Quoc-Hung Nguyen, L. V\'eron; {\em Quasilinear and Hessian type equations with exponential reaction and measure data,}  Archive for Rational Mechanics and Analysis, 214,  235-267 (2014).

 1) M. F. Bidaut-V\'eron, Quoc-Hung Nguyen, L. V\'eron; {\em Quasilinear Lane-Emden equations with absorption and measure data,} Journal de mathematiques pures et appliqu\'ees, 102, 315-337 (2014).