arXiv subjects

Dáithí Ó hAodha

Publications and source records attributed to Dáithí Ó hAodha.

4 recordsLinked to original sources

arXiv2024

Optimal Decay Estimates for the Radially Symmetric Compressible Navier-Stokes Equations

We examine the large-time behaviour of solutions to the compressible Navier-Stokes equations under the assumption of radial symmetry. In particular, we calculate a fast time-decay estimate of the norm of the nonlinear part of the solution. This allows us to obtain a bound from below for the time-decay of the solution in $L^\infty$, proving that our decay estimate in that space is sharp. The decay rate is the same as that of the linear problem for curl-free flow. We also obtain an estimate for a scalar system related to curl-free solutions to the compressible Navier-Stokes equations in a weighted Lebesgue space.

math.AP↗

arXiv2023

Global existence of solutions to the compressible Navier-Stokes equations in weighted Besov spaces

We prove global existence of solutions to the Cauchy problem for the compressible Navier-Stokes equations in Euclidean spaces, given initial data with small norms in Besov and critical weighted Besov spaces. Global existence and a priori bounds in these spaces are obtained for dimension $d\geq 3$.

math.AP↗

arXiv2023

Optimality of the Decay Estimate of Solutions to the Linearised Curl-Free Compressible Navier-Stokes Equations

We discuss optimal estimates of solutions to the compressible Navier-Stokes equations in Besov norms. In particular, we consider the estimate of the curl-free part of the solution to the linearised equations, in the homogeneous case. We prove that our estimate is optimal in the $L^\infty$-norm by showing that the norm is bounded from below by the same decay rate.

math.AP↗

arXiv2021

Large-Time Behaviour of Solutions to the Surface Quasi-Geostrophic Equations

We construct a linear approximation of the solution to the Surface Quasi-Geostrophic Equation in $\mathbb{R}^2$, and obtain a convergence rate in $L^p$ between the solution and this approximation with respect to time. We also demonstrate that the nonlinear term of the solution is bounded sharply in $L^p$ by the same function of time.

math.AP↗