For the 2D free-boundary Euler equations with surface tension on a droplet, there exist arbitrarily small initial velocities such that the vorticity Hessian grows at least exponentially in time.
Para-differential Calculus on Compact Lie Groups and Spherical Capillary Water Waves
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
This paper provides a para-differential calculus toolbox on compact Lie groups and homogeneous spaces. It helps to understand non-local, nonlinear partial differential operators with low regularity on manifolds with high symmetry. In particular, the paper provides a para-linearization formula for the Dirichlet-Neumann operator of a distorted 2-sphere, a key ingredient in understanding long-time behaviour of spherical capillary water waves. As an initial application, the paper provides a new proof of local well-posedness for spherical capillary water waves equation under weaker regularity assumptions compared to previous results.
citation-role summary
background 1
citation-polarity summary
fields
math.AP 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions
For the 2D free-boundary Euler equations with surface tension on a droplet, there exist arbitrarily small initial velocities such that the vorticity Hessian grows at least exponentially in time.