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Tomoaki Yoshizawa

Publications and source records attributed to Tomoaki Yoshizawa.

3 recordsLinked to original sources
arXiv2026

Lower bounds for the lifespan of solutions to the Euler--Korteweg equations

We consider the initial value problem for the Euler--Korteweg equations in the class of irrotational flows. In every space dimension $d \geqslant 2$, we establish a quantitative lower bound for the lifespan of solutions that explicitly exhibits its dependence on the Weber number, the Mach number, and the Sobolev norm of the initial perturbation. In particular, this lower bound can be taken arbitrarily large in a low-Weber-number regime under a suitable algebraic relation between the Mach and Weber numbers.

math.AP↗
arXiv2026

Temporal decay estimates for global solutions of the Navier-Stokes equations with the Coriolis force

We consider temporal decay estimates for global solutions of the Navier-Stokes equations with the Coriolis force. We show that under several conditions including the smallness of the initial data, the solution decays as fast as the corresponding linearized solutions, and its decay rate is higher than expected from the flow of the heat equation. The estimates are derived for all $L^p$-norms with $p\in[2, \infty].$

math.AP↗
arXiv2026

Global well-posedness and temporal decay estimates for the viscous $β$-plane equations

We consider the Cauchy problem of the viscous $β$-plane equations. We first establish the global well-posedness of the system for the initial data sufficiently small compared to the Rossby parameter. The smoothing effect of the flow is then proved, and it is shown that the obtained global solution satisfies the equation in the classical sense. We also reveal that under some additional assumptions, the solution decays as fast as the corresponding linear solution and asymptotically behaves like a constant multiple of the integral kernel of the linearized equation. In particular, the decay rate of the solution is faster than expected from the flow of the heat equation.

math.AP↗