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##### IMI(Institute of Mathematics for Industry)

# Publications

## MI Preprints

2019-2

Title：One-parameter families of Legendre curves and plane line congruences

Author : Yutaro Kabata & Masatomo Takahashi

Author : Yutaro Kabata & Masatomo Takahashi

Abstract: Families of curves in the Euclidean plane naturally contain singular curves, where the frame of classical differential geometry does not work well. We introduce the notions of one-parameter family of Legendre curves in the Euclidean plane, congruent equivalence and curvature. Especially, a one-parameter family of Legendre curves can contain singular curves, and is determined by the curvature up to congruence. We also give properties of one-parameter families of Legendre curves. As applications, we give a relation between one-parameter families of Legendre curves and Legendre surfaces. Moreover, we study plane line congruences (one parameter families of lines in plane) in terms of the curvatures as one-parameter families of Legendre curves.

File：
2019-2

2019-1

Title：Long time existence and the asymptotic behavior of solutions for the 2D quasi-geostrophic equation with large dispersive forcing

Author : Mikihiro Fujii

Author : Mikihiro Fujii

Abstract: We consider the initial value problem of the 2D dispersive quasi-geostrophic equation. We prove the long time existence of the solution for given initial data satisfying the same regularity assumption for the local well-posedness. Moreover, we show that the solution converges to the corresponding linear dispersive solution when the size of dispersion parameter goes to infinity.

File：
2019-1