## Seminar information archive

Seminar information archive ～02/22｜Today's seminar 02/23 | Future seminars 02/24～

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Holomorphic curves into algebraic varieties

**Min Ru**(Houston)Holomorphic curves into algebraic varieties

### 2004/12/15

#### PDE Real Analysis Seminar

10:30-12:45 Room #122 (Graduate School of Math. Sci. Bldg.)

Hamilton-Jacobi-Bellman equations for optimal control of stochastic Navier-Stokes equations.

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

A GEOMETRICAL APPROACH TO FRONT PROPAGATION PROBLEMS IN BOUNDED DOMAINS WITH NEUMANN-TYPE BOUNDARY AND APPLICATIONS

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

**Andrzej Swiech**(ジョージア工科大学) 10:30-11:30Hamilton-Jacobi-Bellman equations for optimal control of stochastic Navier-Stokes equations.

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

**Francesca Da Lio**(Dipartimento di Matematica P. e A.Universit di Padova researcher) 11:45-12:45A GEOMETRICAL APPROACH TO FRONT PROPAGATION PROBLEMS IN BOUNDED DOMAINS WITH NEUMANN-TYPE BOUNDARY AND APPLICATIONS

[ Abstract ]

We talk about a new definition of weak solution for the global-in-time motion of a front in bounded domains with normal velocity depending not only on its curvature but also on the measure of the set it encloses and with a contact angle boundary condition. We apply this definition to study the asymptotic behaviour of the solutions of some local and nonlocal reaction-diffusion equations.

[ Reference URL ]We talk about a new definition of weak solution for the global-in-time motion of a front in bounded domains with normal velocity depending not only on its curvature but also on the measure of the set it encloses and with a contact angle boundary condition. We apply this definition to study the asymptotic behaviour of the solutions of some local and nonlocal reaction-diffusion equations.

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2004/12/13

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

正則曲線、小林双曲性とアーベル多様体の川又特徴付け

**野口潤次郎**(東大数理)正則曲線、小林双曲性とアーベル多様体の川又特徴付け

### 2004/12/01

#### PDE Real Analysis Seminar

10:30-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

A remark on continuous, nowhere differentiable functions

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

**岡本 久**(京都大学)A remark on continuous, nowhere differentiable functions

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2004/10/20

#### PDE Real Analysis Seminar

10:30-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

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.)

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.)

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.)

what (JAPANESE)

**who**(where)what (JAPANESE)

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