We provide a complete local well-posedness theory in $ H^ s $ based Sobolev spaces for
the free boundary incompressible Euler equations with zero surface tension on a connected …

We prove a continuation criterion for the free boundary problem of three-dimensional
incompressible ideal magnetohydrodynamic (MHD) equations in a bounded domain, which …

We study the motion of charged liquid drop in three dimensions where the equations of
motions are given by the Euler equations with free boundary with an electric field. This is a …

arXiv:1907.08192v1 [math.AP] 18 Jul 2019 Page 1 arXiv:1907.08192v1 [math.AP] 18 Jul
2019 DYNAMICAL RELATIVISTIC LIQUID BODIES TODD A. OLIYNYK Abstract. We …

We prove a long-term regularity result for three-dimensional gravity water waves with small
initial data but nonzero initial vorticity. We consider solutions whose vorticity vanishes on the …

It is shown in Ferrari [Comm. Math. Phys., 155 (1993), pp. 277–294] that if is the maximal
time interval of existence of a smooth solution of the incompressible Euler equations in a …

This thesis provides a detailed account of several novel methods and ideas developed by
the author and collaborators to study the low regularity dynamics for a diverse selection of …

We study the motion of charged liquid drop in three dimensions where the equations of
motions are given by the Euler equations with free boundary with an electric field. This is a …

We consider the motion of a perfect uid body in vaccuum with no surface tension, in two
settings. First, we study the motion of a compressible liquid occupying a bounded region of …