Quasi‐Lipschitz condition in potential theory
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AbstractThe velocity $ \vec v $ of an incompressible flow in a bounded three‐dimensional domain is represented by its vorticity $ \vec j $ with the help of an apparently new representation formula. Using this formula we prove a quasi‐Lipschitz estimate for $ \vec v $ in dependence of the supremum norm of $ \vec j $. Our quasi‐Lipschitz bound extends to the case where $ \vec v $ is represented by any continuous $ \vec j $ ≠ rot $ \vec v $
- University of Paderborn Germany
Integral representations, integral operators, integral equations methods in higher dimensions, incompressible flows, Free-surface potential flows for incompressible inviscid fluids, Connections of harmonic functions with differential equations in higher dimensions, PDEs in connection with fluid mechanics, potential theory, Boundary value problems for second-order elliptic equations, compressible flows in \(\mathbb{R}^3\), Systems of elliptic equations, boundary value problems, multiple connected domains in \(\mathbb{R}^3\), quasi-Lipschitz condition
Integral representations, integral operators, integral equations methods in higher dimensions, incompressible flows, Free-surface potential flows for incompressible inviscid fluids, Connections of harmonic functions with differential equations in higher dimensions, PDEs in connection with fluid mechanics, potential theory, Boundary value problems for second-order elliptic equations, compressible flows in \(\mathbb{R}^3\), Systems of elliptic equations, boundary value problems, multiple connected domains in \(\mathbb{R}^3\), quasi-Lipschitz condition
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