On the uniqueness and regularity of the Primitive Equations imposing additional anisotropic regularity
Copyright policy )On the uniqueness and regularity of the Primitive Equations imposing additional anisotropic regularity
In this note, we prove that given u a weak solution of the Primitive Equations, imposing an additional condition on the vertical derivative of the velocity u (concretely ∂zu ∈ L∞(0, T;L2(Ω)) ∩ L2(0, T; H1(Ω))), then two different results hold; namely, uniqueness of weak solution (any weak solution associated to the same data that u must coincide with u) and global in time strong regularity for u (without “smallness assumptions” on the data). Both results are proved when either Dirichlet or Robin type conditions on the bottom are considered. In the last case, a domain with a strictly bounded from below depth has to be imposed, even for the uniqueness result.
Ministerio de Educación y Ciencia
- University of Seville Spain
Anisotropic estimates, Hydrology, hydrography, oceanography, anisotropic estimates, primitive equations, Applied Mathematics, Strong solution, Primitive Equations, General theory of rotating fluids, PDEs in connection with fluid mechanics, Meteorology and atmospheric physics, Weak-strong uniqueness, strong solution, Weak–strong uniqueness, Existence, uniqueness, and regularity theory for incompressible viscous fluids
Anisotropic estimates, Hydrology, hydrography, oceanography, anisotropic estimates, primitive equations, Applied Mathematics, Strong solution, Primitive Equations, General theory of rotating fluids, PDEs in connection with fluid mechanics, Meteorology and atmospheric physics, Weak-strong uniqueness, strong solution, Weak–strong uniqueness, Existence, uniqueness, and regularity theory for incompressible viscous fluids
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