arXiv subjects

Jae Ho Choi

Publications and source records attributed to Jae Ho Choi.

3 recordsLinked to original sources

arXiv2026

Critical global well-posedness for the two-phase Brinkman problem with surface tension

We study a system in which a fluid occupying a bounded simply connected region in $\mathbb{R}^{2}$ is surrounded by another fluid with sharp boundary. They are incompressible Brinkman flows of the same viscosity saturating a porous medium with constant permeability. They interact via surface tension on their interface. We assume that the velocity has no jump across the interface and decays at infinity. We establish the asymptotic stability of the circular interface, which is a steady-state solution to our system. The technical threshold for the size of the initial perturbation for asymptotic stability can be explicitly calculated. We further show that the initial perturbation decays exponentially. We prove the existence, uniqueness, and continuous dependence on initial data of highly regular solutions by containing the perturbation variable in a Wiener-type algebra with a time-activated exponential weight, which allows for analytic solutions with much coarser initial data. The solution is contained in the Wiener-type algebra with the critical scaling exponent for our problem.

math.AP↗

arXiv2026

Traveling wave solutions to a general incompressible Navier-Stokes-Fourier system with free boundary

We study traveling wave solutions to the free boundary problem associated to a generalized Navier-Stokes Fourier system, which models a viscous, incompressible, heat-conducting fluid. The fluid is assumed to occupy a horizontally infinite strip-like domain with flat rigid bottom and moving upper surface. The fluid is acted upon by gravity as well as external sources of bulk force and boundary stress and an external heat source. Additionally, we allow for temperature-dependent viscosity and capillary coefficients, the latter of which gives rise to Marangoni stresses on the free surface. We develop a small data well-posedness theory in Sobolev spaces that shows that if the sources of force, stress, and heat are small, then there exists a unique solution depending continuously on these data.

math.AP↗

arXiv2024

Stability of a Two-Phase Stokes Problem with Surface Tension

In this work, we study the well-posedness of a system of partial differential equations that model the dynamics of a two-dimensional Stokes bubble immersed in two-dimensional ambient Stokes fluid of the same viscosity that extends to infinity under the effect of surface tension. We assume that the two fluids are immiscible and incompressible and that there is no interfacial jump in the fluid velocity. For this PDE system, a circular fluid bubble is a steady-state solution. Given an initial contour for the fluid bubble which is sufficiently close to a circle, we show that there exists a unique, global-in-time solution. This unique solution decays to a circle exponentially fast, which means that circular fluid bubbles are stable steady-state solutions. We also obtain a result concerning the regularity of the unique solution, that although the initial perturbation around a circular contour is assumed to be of low regularity, any later perturbation becomes real analytic, hence smooth.

math.AP↗