| Week 1: March 10 to 14 |
School
"Around Vortices" |
| Week 2: March 17 to 21 |
School
"Around Vortices" |
| Week 3: March 24
to 28 |
Seminar
When:
Date > Tue (Mar
25)
Time >
14:00 to 15:00
Where: Auditorium
3
Speaker:
Miles Wheeler (Brown
University)
Title: Large-amplitude solitary waves with
vorticity
Abstract: The
water wave equations describe the motion of an
incompressible inviscid fluid under the influence of gravity
which is bounded above by a free surface under constant
(atmospheric) pressure. In this talk, we will construct exact
solitary water waves of large amplitude and with an arbitrary distribution of
vorticity. Starting from a shear flow with a flat free surface, we use a
degree-theoretic continuation argument to construct a global connected set
of symmetric solitary waves of elevation, whose profiles decrease
monotonically on either side of a central crest. We will discuss solitary waves
generated by a non-constant pressure on the free surface.
|
| Week 4: March 31
to April 04 |
Seminar
THIS SEMINAR WAS
CANCELLED
When:
Date > Tue (Apr
01)
Time >
14:00 to 15:00
Where: Auditorium
3
Speaker:
Helena J. Nussenzveig Lopes
(UFRJ)
Title: Convergence of Euler-alpha to Euler
with Dirichlet conditions and indifference to the boundary
layer
Abstract: In this talk we will
discuss a recent result by the author with M. Lopes
Filho, E. Titi and A. Zang concerning the asymptotic
behavior of
solutions of the Euler-alpha system, when the
parameter alpha tends to zero. We study this limit in
a 2D bounded domain with no-slip boundary condition and we prove
that, under suitable hypothesis, the limit satisfies
the incompressible Euler system.
|
| Week 5: April 07 to April 11 |
Seminar
When:
Date > Tue (Apr
08)
Time >
14:00 to 15:00
Where: Auditorium
3
Speaker:
Jean-Pierre Puel (École
Polytechnique, France)
Title: Controllability of fluid flows
Abstract:This presentation will give
an overview on the controllability for fluid flows.
There will be no technical proof. First of all we will
describe in an abstract situation the various concepts
of controllability for evolution equations. We will then present some
problems and results concerning the controllability of
systems modeling fluid flows. First of all we will consider the Euler
equation describing the motion of an incompressible
inviscid fluid.
Then we will give some results concerning the
Navier-Stokes equations, modeling an incompressible
viscous fluid, and some related systems, in particular
the case of what is called Lagrangian control and which
might lead to a lot of developments. Finally, we will present a
first result of controllability for the case of a
compressible fluid (in dimension 1) and some important
open problems.
|
| Week 6: April 14 to April 18 |
Seminar
When:
Date > Tue (Apr
15)
Time >
14:00 to 15:00
Where: Auditorium
3
Speaker: Dimitry S. Agafontsev (P.P. Shirshov Institute of
Oceanology of the Russian Academy of Sciences)
Title: On
the singularities development in the framework of 3D Euler
equations
Abstract: We study numerically development of
singularities of vorticity field for 3D Euler equations on
grids of up to 2048^3 nodes. We examine nearly arbitrary
smooth symmetric and non-symmetric initial data. For
several realizations of the initial data - both symmetric
and non-symmetric - and as long as our simulations are
reliable we observe development of singularities when
absolute maximum value of vorticity increases with time
exponentially. Geometric characteristics of singularity
regions also develop exponentially and close to
self-similar way. In addition we observe evolution of
local maximums for vorticity field and those with
sufficiently high vorticity also develop exponentially.
Our results strongly suggest that in the framework of 3D
ideal incompressible hydrodynamics smooth initial data may
generate singularities of vorticity field and that these
singularities develop exponentially. |
| Week 7: April 21 to April 25 |
NO
SEMINAR DUE TO HOLIDAY
|
| Week 8: April 28 to May 02 |
EXCEPTIONALLY, DUE TO
THURSDAY-FRIDAY HOLIDAY
THIS SEMINAR
WILL BE HELD WEDNESDAY, 15-16:00, ROOM 333
Seminar
When:
Date > Wed (Apr
30)
Time >
15:00 to 16:00
Where: Room 333
Speaker: Jinkai Li (Weizmann
Institute)
Title: On
the singularities development in the framework of 3D
Euler equations
Abstract: In
this talk I will discuss the local well-posedness of
strong solutions to the Ericksen-Leslie system modeling the evolution of nematic
liquid crystals. Local well-posedness of strong
solutions to this system is obtained by using the Ginzburg-Landau
approximation. Several blow-up criteria are established
to characterize the maximal existence time of strong solutions
to the Ericksen-Leslie system. It is shown that the
Ginzburg-Landau system strongly converges to the Ericksen-Leslie
system up to the maximal existence time of the strong
solutions of the Ericksen-Leslie system.
|
Week 9: May 05 to May 09
|
Seminar
When:
Date > Tue (May
06)
Time >
14:00 to 15:00
Where: Auditorium
3
Speaker: Yanqiu Guo (Weizmann
Institute)
Title: Persistency
of analyticity for nonlinear wave equations and the cubic
Szego equation
Abstract: Gevrey classes were introduced by Maurice
Gevrey in 1918 to generalize real analytic functions.
Functions of Gevrey classes can be characterized by an
exponential decay of their Fourier coefficients. This
characterization has been proved useful for studying
analytic solutions of various nonlinear PDEs, since the
work by Foias and Temam (1989) on the Navier-Stokes
equations. We use this technique to investigate the
persistency of spatial analyticity for nonlinear wave
equations (joint work with Edriss S. Titi), and the cubic
Szego equation (joint work with Patrick Gerard and Edriss
S. Titi). An advantage of this method is that it provides
a lower bound for the radius of the spatial analyticity of
the solutions. |
| Week 10: May 12 to May 16 |
EXCEPTIONALLY, THIS WEEK THERE WILL
BE NO SEMINAR. INSTEAD, LECTURE 1 OF THE MINICOURSE WILL
BE HELD ON Tueday, MAY 13, Auditorium 3. |
| Week 11: May 19 to May 23 |
Seminar
THIS WEEK THERE
WILL BE TWO SEMINARS, HELD AT THE FEDERAL UNIVERSITY OF
RIO DE JANEIRO
When:
Date > Tue (May
20)
Where: Room
C-119 -- Institute of Mathematics, Universidade Federal
do Rio de Janeiro
Time > 10:00 to 11:00
Speaker: Maria
Schonbek (University of California, Santa Cruz)
Title: L^2 ASYMPTOTIC STABILITY OF MILD
SOLUTIONS TO THE NAVIER-STOKES SYSTEM
Abstract: We consider the initial value problem for
the Navier-Stokes equations modeling an incompressible
fluid in three dimensions:
u_t + u \cdot \nabla u + \nabla p = \Delta u + F,
(x,t) \in R^3 \times (0,\infty)
div u = 0
u(x,0) = u_0(x).
It is well-known that this problem has a unique
global-in-time mild solution for a sufficiently small
initial condition and for a small
external force in suitable scaling invariant spaces.
We show that these global-in-time mild solutions are
asymptotically stable under every (arbitrary large)
L^2-perturbation of their initial conditions.
Time > 13:00 to 14:00
Speaker:
Claude Bardos
(University of Paris 7—Denis Diderot (emeritus);
Laboratory Jacques Louis Lions University of Paris
6—Pierre and Marie Curie; the Wolfgang Pauli Institute in
Vienna.)
Title: DIFFUSION APPROXIMATION FOR STRONGLY HETEROGENEOUS
DIFFUSION MEDIA
Abstract: In this talk, which in particular is a
review of a joint project with Etienne Bernard , François
Golse and Rémi Sentis, I will revisit classical and more
recent methods concerning the diffusion approximation of
the linearized Boltzmann equation in strongly Heterogenous
Media. It gives an opportunity to introduce the moment
method.
Eventually remarks to the derivation from the
billard dynamic will be given.
|
| Week 12: May 26 to May 30 |
4th.
Workshop on Fluids and PDE |
| Week 13: June 02 to June 06 |
Seminar
When:
Date > Tue (June
03)
Time >
***15:30 to 16:30 SPECIAL TIME
Where: Room 228 SPECIAL ROOM
Speaker: Edriss S. Titi (Weizmann
Institute of Science and University of California -
Irvine)
Title: Dynamical
Systems Approach to Turbulence
Abstract: In this talk we will survey the dynamical
systems approach for investigating turbulent flows.
Moreover, we will implement this dynamical systems
framework to design finite parameters feedback control and
data assimilation algorithms. |
Week 14: June 09 to June 13
|
NO FORMAL ACTIVITIES
DURING THIS LAST WEEK |