Year: 2026
Type: preprint
Abstract: We study the free-boundary Euler--Monge--Ampère system as a conservative relaxation of ideal incompressible fluid motion. The force is determined on the actual fluid domain by a Monge--Ampère equation coupled to a nonlinear boundary condition. For each fixed relaxation parameter, we establish local well-posedness for uniformly convex initial domains of class $C^{2,α}$, densities in $C^{1,α}$, and arbitrary initial velocities in $C^{2,α}$. The solution retains these spatial regularities, and the force potential belongs to $C^{3,α}$ up to the moving boundary. Within uniformly bounded data families, the solution depends continuously on the initial data at every lower Hölder exponent.
Source: arXiv (Cornell University)
Authors: Liu, Sicheng, Luo, Tao
Institutions: Ningbo University, City University of Hong Kong
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Ningbo University
OpenAlex ID: W7213403120