DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 34(8) 3155-3170 2014年8月 [査読有り]
Steady-states and traveling-waves of the generalized Constantin Lax-Majda equation are computed and their asymptotic behavior is described. Their relation with possible blow-up and the Benjamin-Ono equation is discussed.
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN 65(4) 1079-1099 2013年10月 [査読有り]
Two partial differential equations are studied from the viewpoint of critical exponents. They are equations for a scalar unknown of one spatial variable, and produce self-similar solutions of the Navier-Stokes equations. Global existence and blow-...
IMA JOURNAL OF APPLIED MATHEMATICS 78(2) 379-403 2013年4月 [査読有り]
We consider the generalized Proudman-Johnson equation with an external force. Solving its steady states numerically, we demonstrate that a unimodal pattern appears at large Reynolds numbers if and only if the parameter endowed in the equation is e...
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...