
Hao
Jia CV 

Contact
Info:
Email: jia@umn.edu Office Hours:Monday 3:30pm4:30pm, Wednesday 2:30pm3:30pm, 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. Courses:MATH 8590 Topics in P.D.E., Fall 2019 MATH8583 Partial Differential equations, Fall 2018 and
Spring 2019 MATH 4242, Spring 2018 MATH4242, Fall 2017 Previous courses at University of Chicago include: 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: google scholar20. Axisymmetrization near point vortex solutions for
the 2D Euler equation, (joint with A. Ionescu), arXiv
1904.09170 19. Linear inviscid damping in Gevrey spaces, ARMA.
online,
see
also arXiv:1904.01188 18. Linear Inviscid damping near monotone shear flows,
preprint arXiv:1902.06849 17. Inviscid damping near the Couette flow in a
channel, (joint with A. Ionescu), Comm. Math Phys.
online,
see also 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, 598611
pdf 15. On the De Gregorio modification of the
ConstantinLaxMajda Model, (joint with S. Stewart and
V. Sverak), ARMA, 2019, 231 (2),
12691304, 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
Amer. J. Math, 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), IMRN,
2018 (22), 69617025, 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, 798862, 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), IMRN, Vol. 2017, No. 19, pp.
59776035, 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 15211603, 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 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) LinksDisclaimer: The views and opinions
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author. The contents of this page have not been
reviewed or approved by the University of Minnesota. 