Michael S. Jolly
Department of Mathematics
Indiana University
Bloomington, IN 47405
phone: 812-855-8865
fax: 812-855-0046
msjolly@indiana.edu
Cover Figure A rendition of the Oseberg Ship is formed by
invariant manifolds of the Kuramoto-Sivashinsky equation. The hull
is in red, the sail in yellow, and the tent in blue. A greater portion
of the side of the tent in the background is constructed, forming
a sea. (parameter value, alpha=32.8)
Teaching, Office Hours: T 1:30-3:30, W 2-14, and R 11-1.
Teaching Materials
Undergraduate Program
Research Interests:
- Turbulence
- Computation of Global Attractors
- Computation of Invariant Manifolds
- Global Bifurcations
Recent Research Papers:
Click on a paper of interest for a short description and/or for the option of
receiving the pdf/postscript file.
- Relations between energy and enstrophy in the global
attractor of the 2-D Navier-Stokes equations
PDF
R. Dascaliuc, C. Foias , and M.S. Jolly
J. Dynamics Differential Equations (accepted) 2005
- Kolmogorov theory via finite time averages
PDF
C. Foias , M.S. Jolly, O.P. Manley, R. Rosa, and R. Temam
Physica D (accepted) 2005
- Kraichnan turbulence via finite time averages
PDF
PS
C. Foias , M.S. Jolly and O.P. Manley
Comm. Math. Phys. Vol. 255, pp. 329--361 2005
- Computation of non-smooth local center manifolds
PDF
PS
M.S. Jolly and R. Rosa
IMA J. Numerical Analysis (accepted) 2003
- On the behavior of the Lorenz equation backward in time
PDF
PS
C. Foias and M. S. Jolly
Vol. 208, pp. 430--448 2005
- Recurrence in the 2-D Navier-Stokes equations
PDF
PS
C. Foias, M. S. Jolly, O. P. Manley,
Discr. & Cont. Dyn. Sys. Vol. 10, pp. 253--268, 2004
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On the Landau-Lifschitz degrees of freedom in 2-D turbulence
C. Foias, M. S. Jolly, O. P. Manley, and R. Rosa
J. Stat. Phys., Vol. 111, pp. 1017-1019 2003
-
Statistical Estimates for the Navier-Stokes Equations
and the Kraichnan Theory of 2-D Fully Developed Turbulence
C. Foias, M. S. Jolly, O. P. Manley, and R. Rosa
J. Stat. Phys., Vol. 108, pp. 591-645 2002
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Nevalinna-Pick interpolation of attractors
C. Foias, M.S. Jolly, W.-S. Li,
Nonlinearity, Vol. 15, pp. 1881-1903 2002
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The Lorenz equation as a metaphor for the Navier-Stokes equations
C. Foias, M.S. Jolly, I. Kukavica and E.S. Titi,
Discrete & Continuous Dynamical Systems, Vol. 7, pp. 403-430 2001
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Dynamic behavior for an iterative viscosity, IMA preprint #1673
C. Foias, M.S. Jolly and O.P. Manley,
RAIRO Model. Math. Model. Anal. Numer., Vol. 34, pp. 353-376 2000
-
The Oseberg transition: visualization of global bifurcations for the
Kuramoto-Sivashinsky equation, IMA preprint #1674
M.E. Johnson, M.S. Jolly and I.G. Kevrekidis
Int. J. Bifurcations & Chaos, Vol. 11, pp. 1-18 2001,
Some figures
- Evaluating
the dimension of an inertial manifold for the Kuramoto-Sivashinsky equation, IMA preprint #1635
M.S. Jolly, R. Rosa and R. Temam
Advances in Differential Equations vol. 5, pp. 31-66 2000
- Accurate computations
on inertial manifolds, IMA preprint #1602
M.S. Jolly, R. Rosa and R. Temam
SIAM J. of Scientific Computing, Vol. 22, pp. 2216-2238 2001
- Two-dimensional invariant manifolds and global
bifurcations: some approximation and visualization studies
M.E. Johnson, M.S. Jolly and
I.G. Kevrekidis Numerical Algorithms 14
1997
- Localization of attractors by their analytic
properties
C. Foias, M.S. Jolly and I. Kukavica
Nonlinearity 9 1996
- On the numerical algebraic approximation
of
attractors
C. Foias and M.S. Jolly
Nonlinearity 8 1995
Acknowledgements: The research described in this web site was undertaken
with the support of the National Science Foundation Grant Numbers
DMS-9404340, DMS-9706903, DMS-0074460, and DMS-0139874.
Computational work was carried out using
facilities provided under NSF Grant Number CDA-9601632.
