A single-exponential growth estimate of the solutions to the 2-dimensional Navier-Stokes equations in the whole space for nondecaying initial velocity is established. The crucial idea is to decompose velocity into high and low frequency parts. Mor...

The Navier-Stokes equations with bounded initial data admit unique local-in-time smooth mild solutions. It is shown that the solution can be extended globally-in-time, if the initial velocity has a special structure. Thanks to the structure, the a...

Discrete and Continuous Dynamical Systems - Series S 6 1409-1415 Oct 2013

The Cauchy problem of the Euler equations is considered with initial data with possibly less regularity. The time-local existence and the uniqueness of strong solutions were established by Pak-Park, when the initial velocity is in the Besov space ...

Journal of Mathematical Analysis and Applications 312 1-13 Dec 2005

On this paper spatial analyticity of solutions to the nonstationary incompressive Navier-Stokes flow in Ḣn/2-1 (ℝRn) is established. The proof is based on the estimates for the higher order derivatives of solutions. These estimates imply not only ...

Journal of Functional Analysis 260 2148-2162 Apr 2011

The Cauchy problem of the Euler equations in the whole space is considered with non-decaying initial velocity in the frame work of B∞,1 1. It is proved that if the initial velocity is real analytic then the solution is also real analytic in spatia...

We study the mathematical analysis of the spin-coat model withthe heat convection. We propose the suitable model, and proved the local existence and uniqueness of mild solutions to the rotating Navier-Stokes equations coupled with the heat transpo...

Mathematical Analysis of spin-coat

Japan Society for the Promotion of Science: Grants-in-Aid for Scientific Research

Project Year: Aug 2011 - Mar 2013

Mathematical Anaysis for fluid dynamics model of spin-coat

Japan Society for the Promotion of Science: Grants-in-Aid for Scientific Research