# 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,

multiscale

atmospheric dynamics and turbulence, high resolution

simulations.

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

incompressible

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 L

^{3}. 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.