過去の記録

過去の記録 ~02/20本日 02/21 | 今後の予定 02/22~

2004年12月01日(水)

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 122号室
岡本 久 氏 (京都大学)
A remark on continuous, nowhere differentiable functions
[ 講演概要 ]
We consider a parameterized family of continuous functions, which containsas its members Bourbai's and Perkins's nowhere differentiable functions as well as the Cantor-Lebesgue singular functions.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

2004年10月20日(水)

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 122号室
Hermann Sohr 氏 (University of Paderborn)
Some recent results on the Navier-Stokes equations
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

2004年10月13日(水)

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 128号室
Philippe G. LeFloch 氏 (University of Paris 6)
Existence, uniqueness, and continuous dependence of entropy solutions to hyperbolic systems
[ 講演概要 ]
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).
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

2004年09月29日(水)

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 117号室
Alex Mahalov 氏 (Arizona State University)
Global Regularity of the 3D Navier-Stokes with Uniformly Large Initial Vorticity
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

2004年07月05日(月)

数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室
本セミナーは、グローバルCOE事業「数学新展開の研究教育拠点」(東京大学)の援助を受け、GCOEセミナーして行われています。
http://www.ms.u-tokyo.ac.jp/gcoe/index.html

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