Navier-Stokes equations

Thursday, June 23, 2016 - 10:15am - 11:05am
Martine Marion (École Centrale de Lyon)
We consider combustion problems in the presence of complex chemistry and nonlinear diffusion laws leading to fully nonlinear multispecies reaction-diffusion equations. We establish results of existence of solution and maximum principle, i.e. positivity of the mass fractions, which rely on specific properties of the models. The nonlinear diffusion coefficients are obtained by resolution of the so-called Stefan-Maxwell equations.
Thursday, February 25, 2010 - 11:30am - 12:15pm
Igor Kukavica (University of Southern California)
Keywords: Navier-Stokes equations, partial regularity,
Hausdorff dimension, fractal dimension.

Abstract: A classical result of Caffarelli, Kohn, and Nirenberg states
that the one dimensional Hausdorff measure of singularities
of a suitable weak solution of the Navier-Stokes system is
zero. We present a short proof of the partial regularity
result which allows the force to belong to a singular Morrey
space. We also provide a new upper bound for the fractal
dimension of the singular set.
Thursday, February 25, 2010 - 10:00am - 10:45am
Jiahong Wu (Oklahoma State University)
Keywords: fractional Laplace, global regularity, the surface quasi-geostrophic equation

Abstract:Fundamental mathematical issues concerning the
surface quasi-geostrophic (SQG) equation have recently
attracted the attention of many researchers and important
progress has been made. This talk focuses on the existence,
uniqueness and regularity of solutions to the SQG equation
and covers both the inviscid and dissipative cases. We will
summarize some existing work and report very recent
Thursday, February 25, 2010 - 2:00pm - 2:45pm
Gautam Iyer (Stanford University)
Keywords: Navier Stokes, stochastic-Lagrangian, particle method.

Abstract: I will introduce an exact stochastic representation for certain
non-linear transport equations (e.g. 3D-Navier-Stokes, Burgers)
based on noisy Lagrangian paths, and use this to construct a
(stochastic) particle system for the Navier-Stokes equations. On any
fixed time interval, this particle system converges to the
Navier-Stokes equations as the number of particles goes to infinity.
Wednesday, February 24, 2010 - 11:30am - 12:15pm
Alex Mahalov (Arizona State University)
Keywords: 3D Navier-Stokes equations,
atmospheric dynamics and turbulence, high resolution
Wednesday, February 24, 2010 - 9:00am - 9:45am
Zhouping Xin (Chinese University of Hong Kong)
Keywords: Viscous boundary layers, Prandtl's boundary layer system,
Navier-slip bounadry conditions, incompressible Navier-Stokes system.
Tuesday, February 23, 2010 - 2:00pm - 2:45pm
Tai-Peng Tsai (University of British Columbia)
Keywords: Asymptotics, Exterior flows, Navier-Stokes equations, self-similar

Abstract: We prove the unique existence of solutions of the 3D
Navier-Stokes equations in an exterior domain with small
non-decaying boundary data, for all t ∈ R or t > 0. In
the case t > 0 it is coupled with a small initial data in
weak L3. If the boundary data is time-periodic, the spatial
asymptotics of the time-entire solution is given by a Landau
Monday, February 22, 2010 - 9:00am - 9:45am
Thomas Hou (California Institute of Technology)
Keywords: 3D incompressible Navier-Stokes equations,
finite time blow-up, and global regularity,
and stabilizing effect of convection.

Abstract: We study the singularity formation of a recntly proposed 3D model
for the incompressible Euler and Navier-Stokes equations. This
3D model is derived from the axisymmetric Navier-Stokes equations
with swirl using a set of new variables. The model preserves
almost all the properties of the full 3D Euler or Navier-Stokes
Thursday, June 6, 2013 - 1:45pm - 2:30pm
Fangxu Jing (University of Southern California)
We model various configurations of vortex merger problems for the Navier-Stokes equations using the core growth model for vorticity evolution coupled with the passive particle field and an appropriately chosen time-dependent rotating reference frame. Using the combined tools of analyzing the topology of the streamline patterns along with the careful tracking of passive fields, we highlight the key features of the stages of evolution of vortex merger, pinpointing deficiencies in the low-dimensional model with respect to similar experimental/numerical studies.
Monday, September 24, 2012 - 10:15am - 11:05am
Edriss Titi (Weizmann Institute of Science)
In this talk we will implement the notion of finite number of determining parameters for the long-time dynamics of the Navier-Stokes equations (NSE), such as determining modes, nodes, volume elements, and other determining interpolants, to design finite-dimensional feedback control for stabilizing their solutions. The same approach is found to be applicable for data assimilations.


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