
Hao
Jia CV 

Contact
Info:
Email: jiahao@math.uchicago.edu Office Hours:2:30pm3:30 pm on Monday and Wednesday, or by
appointment. Education: PhD in Mathematics, 20072013, 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. At an early stage of my career, I am open
to various new, exciting directions. Courses:MATH/ 20100  53 Math Methods for Phy. Sci2, Spring
2016 MATH / 15300 49 & 55 Calculus 3,
Autumn 13 MATH / 19520  49 Math Methods for Soc.
Sci, Spring 2014 MATH / 16100 21 Honors Calculus
I, Autumn 2014 MATH / 1620021 Honors Calculus
II, Winter 2015 MATH / 16300  21 Honors Calculus
III, Spring 2015 MATH / 20000  41 Math Methods For Phy. Sci
1, 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 nongeneric 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 353384, see also arXiv:1403.5696 6. Are the incompressible 3d NavierStokes equations locally illposed in the natural energy space? (with V.Sverak), J. Func. Anal., Volume 268, Issue 12, 15 June 2015, pages 37343766, see also arXiv:1306.2136 (pdf) 5. Localinspace estimates near initial time for
weak solutions of NavierStokes
equations and forward selfsimilar solutions (joint with
V.Sverak), Invent. Math. 196 (2014), no.1, 233265
. (pdf) 4. Liouville theorem for timedependent Stokes
system in domains joint with G.Seregin and
V.Sverak {my advisor}), J. Math. Phys. 53, 115604
(2012), (pdf) 2. On scaleinvariant 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
halfspace, (with G.Seregin and V.Sverak) Zap. Nauchn.
Sem. S.Petersburg. Otdel. Mat. Inst. Steklov. (POMI)
410 (2013) LinksDepartment
of Mathematics, University of Chicago 