We consider 1D equations with nonlocal velocity of the form
w(t) + uw(x) delta u(x)w = -v Lambda(gamma)w
where the nonlocal velocity u is given by (1) u = (1-partial derivative(xx))-(beta)w, beta > 0 or (2) u = Hw H is the Hilbert transform). I...
EUROPEAN JOURNAL OF MECHANICS B-FLUIDS 65 234-246 2017年9月 [査読有り]
We consider the Navier-Stokes equations in 2D flat tori. With various external forces and aspect ratios of the tori, we compute steady-states and time-periodic solutions at large Reynolds numbers. Our external forces are more general than those co...
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 33(1) 145-166 2016年2月 [査読有り]
Solutions of a nonlinear heat equation are numerically computed in the time variable t lying in the complex plane, and possible singularities are sought. It turns out that in the complex half plane , where denotes the real part of a complex number...
We study stability and bifurcation of stationary and time-periodic solutions of Kolmogorov's problem for the Navier-Stokes equations in two-dimensional (2D) flat tori. Specifically we look for a unimodal solution, which is characterized by having ...
We consider two-dimensional progressive water-waves, which propagate with a constant speed and a constant shape. Fluid motion is assumed to be irrotational. Trajectories in a coordinate system attached to the wave are easily computed by drawing co...
人文科学研究科
理学部