Rotating Navier-Stokes Equations in $${\mathbb R}^{3}_{+}$$ with Initial Data Nondecreasing at Infinity: The Ekman Boundary Layer Problem |
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Authors: | Yoshikazu Giga Katsuya Inui Alex Mahalov Shin’ya Matsui Jürgen Saal |
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Institution: | Yoshikazu Giga, Katsuya Inui, Alex Mahalov, Shin’ya Matsui and Jürgen Saal |
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Abstract: | We prove time local existence and uniqueness of solutions to a boundary layer problem in a rotating frame around the stationary
solution called the Ekman spiral. We choose initial data in the vector-valued homogeneous Besov space for 2 < p < ∞. Here the L
p
-integrability is imposed in the normal direction, while we may have no decay in tangential components, since the Besov space
contains nondecaying functions such as almost periodic functions. A crucial ingredient is theory for vector-valued homogeneous
Besov spaces. For instance we provide and apply an operator-valued bounded H
∞-calculus for the Laplacian in for a general Banach space . |
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Keywords: | |
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