We consider the incompressible Euler equations on an analytic domain Ω with a nonhomogeneous boundary condition u·n=u¯·n on ∂Ω, where u¯ is a given divergence-free analytic vector field. We establish the local well-posedness for u in analytic spaces without any compatibility conditions in all space dimensions. We also prove the global well-posedness in the 2D case if u¯ decays in time sufficiently fast.
Kukavica, I., Ożański, W., Sammartino, M. (2025). The inviscid inflow-outflow problem via analyticity. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 249(3) [10.1007/s00205-025-02095-y].
The inviscid inflow-outflow problem via analyticity
Sammartino, MarcoUltimo
2025-06-01
Abstract
We consider the incompressible Euler equations on an analytic domain Ω with a nonhomogeneous boundary condition u·n=u¯·n on ∂Ω, where u¯ is a given divergence-free analytic vector field. We establish the local well-posedness for u in analytic spaces without any compatibility conditions in all space dimensions. We also prove the global well-posedness in the 2D case if u¯ decays in time sufficiently fast.
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