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 1pm3pm, Wednesday 2pm3pm, 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.
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. Sci2, 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.
Sci2, 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 / 20100  53 Math Methods For Phy.
Sci2, Spring 2015
MATH / 20000  41 Math Methods For Phy. Sci
1, Autumn 2015
MATH / 20500  55 Analysis in R^n3, Autumn
2015
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, 598611 pdf
15. On the De Gregorio modification of the
ConstantinLaxMajda 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,
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)
3. Minimal L^3 initial data for potential
NavierStokes singularities (joint with V. Sverak ),
SIAM J. Math. Anal. 45 (2013), no.3. See also on arXiv (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)
Links
arxiv
Analysis and PDE
PDE seminar at UMN
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author. The contents of this page have not been
reviewed or approved by the University of Minnesota.
