Hao Jia
CV

 Contact Info

Email: jia@umn.edu
Address: Vincent Hall 235
Department of Mathematics
University of Minnesota
206 Church St. S.E.
Minneapolis, MN 55455

Office Hours:

Monday 1pm-3pm, Wednesday 2pm-3pm, or by appointment

Education:

PhD in Mathematics, 2007-2013, University of Minnesota. Advisor: Vladimir Sverak

Research Interests:

My research interest is mainly in the theory of Partial Differential Equations and Analysis in general. Main topics of my thesis are related to the Navier Stokes Equation. Recently I also become interested in dispersive equations, especially the long time behavior of solutions.

Courses:

MATH8583 Partial Differential equations, Fall 2018 and Spring 2019
course page

MATH 4242, Spring 2018
See Moodle page for more information

MATH4242, Fall 2017
syllabus

Previous courses at University of Chicago include:

MATH/ 20100 - 53 Math Methods for Phy. Sci-2, Spring 2016

MATH / 15300 -49 & 55  Calculus 3,  Autumn 13

MATH / 19520 - 49   Math Methods for Soc. Sci,  Spring 2014
MATH / 20100 - 53   Math Methods For Phy. Sci-2,  Spring 2014

MATH / 16100 -21    Honors Calculus I,  Autumn 2014

MATH / 16200-21     Honors Calculus II, Winter 2015

MATH / 16300 - 21   Honors Calculus III,   Spring 2015
MATH / 20100 - 53   Math Methods For Phy. Sci-2,  Spring 2015

MATH / 20000 - 41   Math Methods For Phy. Sci -1,  Autumn 2015
MATH / 20500 - 55   Analysis in R^n-3, Autumn 2015

Publications: google scholar

17. Inviscid damping near shear flows in a channel, (joint with A. Ionescu), preprint arXiv:1808.04026

16. Asymptotics of stationary Navier Stokes equations in higher dimensions, (joint with V. Sverak), Acta Math Sinica (Engl. Ser.) 34 (2018), no. 4, 598-611 pdf

15. On the De Gregorio modification of the Constantin-Lax-Majda Model, (joint with S. Stewart and V. Sverak), accepted by ARMA,   arXiv:1710.02737

14. Global center stable manifold for the defocusing energy critical wave equation with potential, (joint with B.P. Liu, W. Schlag, G.X. Xu),  accepted by AJM,  arXiv:1706.09284

13. Universality of blow up profile for small blow up solutions to the energy critical wave map equation, (joint with T. Duyckaerts, C. Kenig and F. Merle), to appear IMRN, 50 pages,  arXiv:1612.04927

12. Soliton resolution along a sequence of times for the focusing energy critical wave equation, (joint with T. Duyckaerts, C. Kenig and F. Merle), Geometric and Functional Analysis, Vol 27, Issue 4, 2017, 798-862,  arXiv:1601.01871 

(This paper is an extension of arXiv:1510.00075, in two ways: 1. the global case is now considered, 2. significantly the dispersive error is now shown to vanish asymptotically in energy space. )

11. Soliton resolution along a sequence of times with dispersive error for type II singular solutions to focusing energy critical wave equation, preprint 2015, 42 pages, arXiv:1510.00075

10. Generic and non-generic behavior of solutions to the defocusing energy critical wave equation with potential in the radial case, (Joint with B. Liu, W. Schlag, G. Xu), IMRN, Vol. 2017, No. 19, pp. 5977-6035, see also arXiv 1506.04763

9.  Asymptotic decomposition for semilinear wave and equivariant wave map equations (joint with C. Kenig),  American Journal of Mathematics 139 (2017), pages 1521-1603,  see also arXiv:1503.06715

8.  Uniqueness of solutions to to Navier Stokes equation with small initial data in $L^{3,\infty}(R^3)$,  preprint 2014 arXiv:1409.8382

7.  Long time dynamics of defocusing energy critical 3 + 1 dimensional wave equation with potential in the radial case (joint with Baoping Liu and Guixiang Xu), Comm. Math. Phy., Volume 339, Issue 2, 2015, pages 353-384, see also arXiv:1403.5696

6.  Are the incompressible 3d Navier-Stokes equations locally ill-posed in the natural energy space? (with    V.Sverak),  J. Func. Anal., Volume 268, Issue 12, 15 June 2015, pages 3734-3766, see also arXiv:1306.2136 (pdf)

5.  Local-in-space estimates near initial time for weak solutions of Navier-Stokes    equations and forward self-similar solutions (joint with V.Sverak), Invent. Math. 196 (2014), no.1, 233-265 . (pdf)

4.  Liouville theorem for time-dependent Stokes system in domains joint with G.Seregin and  V.Sverak {my advisor}), J. Math. Phys. 53, 115604 (2012), (pdf)

3.  Minimal L^3 initial data for potential Navier-Stokes singularities (joint with V. Sverak ), SIAM J. Math. Anal. 45 (2013), no.3. See also on arXiv (pdf)

2.  On scale-invariant solutions of Navier Stokes equations (with Vladimir Sverak), Proceedings of the 6th European congress of Mathematicians, krakow 2012.

1.  A Liouville theorem for the Stokes system in half-space, (with G.Seregin and V.Sverak) Zap. Nauchn. Sem. S.-Petersburg. Otdel. Mat. Inst. Steklov. (POMI) 410 (2013)


Links

arxiv Analysis and PDE

PDE seminar at UMN

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