ABSTRACT
We consider a bounded domain https://www.w3.org/1998/Math/MathML"> Ω ∈ ℝ n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203755518/fbcb5fb2-fbc4-4b15-ab17-e703fd7c937e/content/eq1174.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , partially filled with water. The water occupies a fixed part of the domain at an initial time, while the rest is filled with a gas of constant pressure. We assume surface tension at the water-gas interface. Given also an initial velocity distribution we ask how the fluid and the shape of the gas bubble evolve in time.
