Naoto Deguchi | Searcharxiv

arXiv2025

Stability analysis of time-periodic solutions to the Navier-Stokes-Fourier system in 3D whole space

This paper concerns the large-time behavior of perturbations around a time-periodic solution to the Navier-Stokes-Fourier system in the three-dimensional whole space. The time-periodic solution exists when a given external force is small enough. We derive the time-decay estimate of the perturbation under the assumption that an initial perturbation is sufficiently small. The time-space integral estimate for the linearized semigroup around the constant state in the Besov spaces is effectively applied in the proof.

math.AP↗

arXiv2025

Low Mach number limit for the compressible Navier-Stokes equation with a stationary force

In this paper, we are concerned with the low Mach number limit for the compressible Navier-Stokes equation with a stationary force and ill-prepared initial data in the three-dimensional whole space. The convergence result of the stationary solutions toward the corresponding incompressible flow is obtained when the stationary force is small enough. Under the assumption that the initial perturbation around the stationary solution is small enough, the convergence result of the perturbation toward the corresponding perturbation around the stationary incompressible flow is obtained globally in time. The proof relies crucially on the Strichartz type estimate for the linearized semigroup around the motionless state which reflects not only its dispersive property but also dissipative properties of the linearized operator.

math.AP↗