[00196] Recent development of mathematical geophysics
Session Time & Room : 3D (Aug.23, 15:30-17:10) @G710
Type : Proposal of Minisymposium
Abstract : The purpose of this minisymposium is to interact with mathematicians working on geophysics with various recent topics: large time behavior of solutions, machine learning approach, flow behavior on manifolds and meteorological analysis. These each topics have long research history. However, the tendency of the recent studies seems to be a broader point of view, not only from each own research field but also from an interdisciplinary perspective.
[01262] Global solutions for rotating MHD equations in the critical space
Format : Talk at Waseda University
Author(s) :
Ryo Takada (The University of Tokyo)
Keiji Yoneda (Kyushu University)
Abstract : We consider the initial value problem for the incompressible rotating magnetohydrodynamics equations in $\mathbb{R}^3$. We prove the unique existence of global solutions for large initial data in the scaling critical space $\dot{H}^{\frac{1}{2}}(\mathbb{R}^3)$ when the rotation speed is sufficiently high. In order to control large magnetic fields, we introduce a modified linear solution for the velocity, and show its smallness in a suitable space-time norm by means of the dispersive effect of the Coriolis force.
[02684] Multi-scale interaction of tropical weather in a simplified three-dimensional model
Format : Talk at Waseda University
Author(s) :
Daisuke Takasuka (University of Tokyo)
Abstract : In the tropics, various kinds of weather systems are spontaneously realized, as represented by mesoscale convective systems, equatorial waves, the Madden–Julian oscillation ((\rm{MJO})). They interact with each other through moist processes, wave–mean-flow interaction, and so on. As an example of this, we will present a non-linear multi-scale process in the MJO initiation, which involves the mean tropical circulations and equatorial waves, using a simplified three-dimensional fluid dynamical model.
[00606] Eigenvalue Problem for Perturbation Operator of Two-jet Kolmogorov Type Flow
Format : Talk at Waseda University
Author(s) :
Tatsu-Hiko Miura (Hirosaki University)
Abstract : We consider the linear stability of the two-jet Kolmogorov type flow which is a stationary solution to the vorticity equation on the unit sphere given by the zonal spherical harmonic function of degree two. Using the mixing structure of the two-jet Kolmogorov type flow, we show that the perturbation operator does not have eigenvalues except for zero. As an application, we also prove the occurrence of the enhanced dissipation in the linearized setting.
[00377] On the physics-informed neural networks approximating the primitive equations
Format : Online Talk on Zoom
Author(s) :
Quyuan Lin (University of California, Santa Barbara)
Ruimeng Hu (University of California, Santa Barbara)
Alan Raydan (University of California, Santa Barbara)
Sui Tang (University of California, Santa Barbara)
Abstract : Large scale dynamics of the oceans and the atmosphere are governed by the primitive equations (PEs). Due to the nonlinearity and nonlocality, the numerical study of the PEs is in general a hard task. In this talk, I will introduce physics-informed neural networks (PINNs) to tackle this challenge, and show the theoretical error estimates and the results from numerical experiments that confirm the reliability of PINNs.
