arXiv subjects
Publications and source records attributed to Haram Ko.
We consider the compressible Euler equation with a Coriolis term and prove a lower bound on the time of existence of solutions in terms of the speed of rotation, sound speed and size of the initial data. Along the way, we obtain precise dispersive decay estimates for the linearized equation. In the incompressible limit, this improves current bounds for the incompressible Euler-Coriolis system as well.
We investigate and quantify the effect of stratification on the stability time of a stably stratified rest state for the 2D inviscid Boussinesq system on $\mathbb{R}^2$. As an important consequence, we obtain stability of the steady state starting from an $\varepsilon$-sized initial perturbation of Sobolev regularity $H^{3^+}$ on a timescale $\mathcal{O}(\varepsilon^{-4/3})$. In our setting, stratification induces dispersion and at the core of our approach are inhomogeneous Strichartz estimates used to control nonlinear contributions. This allows to keep only $L^2-$based regularity assumptions on the initial perturbation, whereas previous works impose additional localizations to achieve this timescale. We prove the analogous result for the related dispersive SQG equation.
We prove that the solutions to the 3D Navier-Stokes equation with constant rotation exist globally for small axisymmetric initial data, where the smallness is uniform with respect to the viscosity $\nu \in [0,\infty)$. This expands the work by Guo, Pausader, and Widmayer \cite{GPW} which showed the global axisymmetric stability of rotation for 3D incompressible Euler's equation, to the viscous case, but for a single threshold that works for arbitrary viscosity. This is achieved by suitably adapting the dispersive framework established in \cite{GPW} to the Navier-Stokes setting.