Hao Jia
CV

Contact Info

Email: jiahao@math.uchicago.edu
Department of Mathematics
University of Chicago
5734 S. University Ave
Chicago, Illinois 60637

### Office Hours:

2:30pm-3:30 pm on Monday and Wednesday, or by appointment.

Education:

### 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. At an early stage of my career, I am open to various new, exciting directions.

### Courses:

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:

Here you can find some of my work:

12. Soliton resolution along a sequence of times for the focusing energy critical wave equation, (joint with T. Duyckaerts, C. Kenig and F. Merle), preprint 2016, 51 pages,  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), preprint 2015, 44 pages,  arXiv 1506.04763

9.  Asymptotic decomposition for semilinear wave and equivariant wave map equations (joint with C. Kenig),  preprint 2015, 74 pages,  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)