Joint work with Ovidiu Costin, G. Luo.We consider a new approach to a class of evolutionary PDEswhere questionof global existence or lack of it is tied to the asymptoticsof solutionto a non-linear integral equation in a dual variable whosesolution hasbeen shown to exist a priori. This integral equation approachis inspiredby Borel summation of a ...
Creator:
Tanveer, Saleh A. (The Ohio State University)
Created:
2008-07-17
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We prove the unique existence of solutions of the 3DincompressibleNavier-Stokes equations in an exterior domain with smallnon-decaying boundary data, for all t ˆˆ R or t > 0. Inthe case t > 0 it is coupled with a small initial data inweak L3. If the boundary data is time-periodic, the spatialasymptotics of the time-entire solution is given by a ...
Creator:
Tsai, Tai-Peng (University of British Columbia)
Created:
2010-02-23
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 b...
Creator:
Titi, Edriss Saleh (Weizmann Institute of Science)
Created:
2012-09-24
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 car...
Creator:
Jing, Fangxu (University of Southern California)
Created:
2013-06-06
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
High resolution multi-scale simulations of limited area atmospheric environments are one of the major frontiers of atmospheric sciences and environmental sustainability. The latest developments in high performance computing technologies represent an opportunity to advance and improve real time atmospheric characterization and forecasting over li...
Creator:
Mahalov, Alex (Arizona State University)
Created:
2010-02-24
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
A classical result of Caffarelli, Kohn, and Nirenberg statesthat the one dimensional Hausdorff measure of singularitiesof a suitable weak solution of the Navier-Stokes system iszero. We present a short proof of the partial regularityresult which allows the force to belong to a singular Morreyspace. We also provide a new upper bound for the fract...
Creator:
Kukavica, Igor (University of Southern California)
Created:
2010-02-25
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 modelfor the incompressible Euler and Navier-Stokes equations. This3D model is derived from the axisymmetric Navier-Stokes equationswith swirl u...
Creator:
Hou, Thomas Y. (California Institute of Technology)
Created:
2010-02-22
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 inte...
Creator:
Iyer, Gautam (Stanford University)
Created:
2010-02-25
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Fundamental mathematical issues concerning thesurface quasi-geostrophic (SQG) equation have recentlyattracted the attention of many researchers and importantprogress has been made. This talk focuses on the existence,uniqueness and regularity of solutions to the SQG equationand covers both the inviscid and dissipative cases. We willsummarize some...
Creator:
Wu, Jiahong (Oklahoma State University)
Created:
2010-02-25
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In this talk, I will discuss some issues and recent results related to the viscous boundary layer theory. In particular, I will present a global existence result on classical soluition to the 2-dimensional unsteady Prandtl's boundary system; some convergence results on viscous solutions when the viscosity becomes small. Both non-slip and Navier-...
Creator:
Xin, Zhouping (Chinese University of Hong Kong)
Created:
2010-02-24
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.