arXiv subjects

R. McOwen

Publications and source records attributed to R. McOwen.

3 recordsLinked to original sources

arXiv2024

The viscosity limit of fluid flows with growth/decay conditions at infinity

We prove that the Navier-Stokes equation is well-posed in function spaces on $\mathbb{R}^d$, $d\ge 2$, that contain vector fields of order $O(|x|^κ)$ as $|x|\to\infty$ with $κ<1/2$. The corresponding solutions depend continuously on the viscosity parameter $ν\ge 0$ and converge to the solutions of the Euler equation as $ν\to 0+$. Our proof is based on the properties of the conjugated heat flow on weighted Sobolev spaces and on a new variant of the Lie-Trotter product formula for nonlinear semigroups.

math.AP↗

arXiv2022

Spatial asymptotic expansions in the Navier-Stokes equation

We prove that the Navier-Stokes equation for a viscous incompressible fluid in $\mathbb{R}^d$ is locally well-posed in spaces of functions allowing spatial asymptotic expansions with log terms as $|x|\to\infty$ of any a priori given order. The solution depends analytically on the initial data and time so that for any $0<\vartheta<π/2$ it can be holomorphically extended in time to a conic sector in $\mathbb{C}$ with angle $2\vartheta$ at zero. We discuss the approximation of solutions by their asymptotic parts.

math.AP↗

arXiv2016

Spatial asymptotic expansions in the incompressible Euler equation

In this paper we prove that the Euler equation describing the motion of an ideal fluid in $\R^d$ is well-posed in a class of functions allowing spatial asymptotic expansions as $|x|\to\infty$ of any a priori given order. These asymptotic expansions can involve log terms and lead to a family of conservation laws. Typically, the solutions of the Euler equation with initial data in the Schwartz class develop non-trivial spatial asymptotic expansions of the type considered here.

math.AP↗