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Seminar information archive
Seminar information archive ～01/23｜Today's seminar 01/24 | Future seminars 01/25～
2004/10/20
PDE Real Analysis Seminar
10:30-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Hermann Sohr (University of Paderborn)
Some recent results on the Navier-Stokes equations
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Hermann Sohr (University of Paderborn)
Some recent results on the Navier-Stokes equations
[ Abstract ]
The aim of this talk is to explain some new results in particular on local regularity properties of Hopf type weak solutions to the Navier-Stokes equations for arbitrary domains. Further we explain a new existence result for nonhomogeneous data and a result for global regular solutions with "slightly" modified forces.
[ Reference URL ]The aim of this talk is to explain some new results in particular on local regularity properties of Hopf type weak solutions to the Navier-Stokes equations for arbitrary domains. Further we explain a new existence result for nonhomogeneous data and a result for global regular solutions with "slightly" modified forces.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2004/10/13
PDE Real Analysis Seminar
10:30-11:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Philippe G. LeFloch (University of Paris 6)
Existence, uniqueness, and continuous dependence of entropy solutions to hyperbolic systems
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Philippe G. LeFloch (University of Paris 6)
Existence, uniqueness, and continuous dependence of entropy solutions to hyperbolic systems
[ Abstract ]
I will review the well-posedness theory of nonlinear hyperbolic systems, in conservative or in non-conservative form, by focusing attention on the existence and properties of entropy solutions with sufficiently small total variation.
New results and perspectives on the following issues will be discussed: Glimm's existence theorem,
Bressan-LeFloch's uniqueness theorem,and the L1 continuous dependence property (established by Bressan, LeFloch, Liu, and Yang).
[ Reference URL ]I will review the well-posedness theory of nonlinear hyperbolic systems, in conservative or in non-conservative form, by focusing attention on the existence and properties of entropy solutions with sufficiently small total variation.
New results and perspectives on the following issues will be discussed: Glimm's existence theorem,
Bressan-LeFloch's uniqueness theorem,and the L1 continuous dependence property (established by Bressan, LeFloch, Liu, and Yang).
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2004/09/29
PDE Real Analysis Seminar
10:30-11:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Alex Mahalov (Arizona State University)
Global Regularity of the 3D Navier-Stokes with Uniformly Large Initial Vorticity
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Alex Mahalov (Arizona State University)
Global Regularity of the 3D Navier-Stokes with Uniformly Large Initial Vorticity
[ Abstract ]
We prove existence on infinite time intervals of regular solutions to the 3D Navier-Stokes Equations for fully three-dimensional initial data characterized by uniformly large vorticity with periodic boundary conditions and in bounded cylindrical domains; smoothness assumptions for initial data are the same as in local existence theorems. There are no conditional assumptions on the properties of solutions at later times, nor are the global solutions close to any 2D manifold.
The global existence is proven using techniques of fast singular oscillating limits and the Littlewood-Paley dyadic decomposition. The approach is based on the computation of singular limits of rapidly oscillating operators and cancellation of oscillations in the nonlinear interactions for the vorticity field. With nonlinear averaging methods in the context of almost periodic functions, we obtain fully 3D limit resonant Navier-Stokes equations. Using Lemmas on restricted convolutions, we establish the global regularity of the latter without any restriction on the size of 3D initial data.
With strong convergence theorems, we bootstrap this into the global regularity of the 3D Navier-Stokes Equations with uniformly large initial vorticity.
[ Reference URL ]We prove existence on infinite time intervals of regular solutions to the 3D Navier-Stokes Equations for fully three-dimensional initial data characterized by uniformly large vorticity with periodic boundary conditions and in bounded cylindrical domains; smoothness assumptions for initial data are the same as in local existence theorems. There are no conditional assumptions on the properties of solutions at later times, nor are the global solutions close to any 2D manifold.
The global existence is proven using techniques of fast singular oscillating limits and the Littlewood-Paley dyadic decomposition. The approach is based on the computation of singular limits of rapidly oscillating operators and cancellation of oscillations in the nonlinear interactions for the vorticity field. With nonlinear averaging methods in the context of almost periodic functions, we obtain fully 3D limit resonant Navier-Stokes equations. Using Lemmas on restricted convolutions, we establish the global regularity of the latter without any restriction on the size of 3D initial data.
With strong convergence theorems, we bootstrap this into the global regularity of the 3D Navier-Stokes Equations with uniformly large initial vorticity.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2004/07/05
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
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who (where)
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