Year: 2025
Type: article
Abstract: We consider the incompressible Euler equations on an analytic domain $$\Omega $$ Ω with a nonhomogeneous boundary condition $$u\cdot {\textsf{n}} = {\overline{u}}\cdot {\textsf{n}}$$ u · n = u ¯ · n on $$\partial \Omega $$ ∂ Ω , where $${\overline{u}}$$ 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 $${\overline{u}}$$ u ¯ decays in time sufficiently fast.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4409431276