Rotating Navier-Stokes Equations in $${\mathbb R}^{3}_{+}$$ with Initial Data Nondecreasing at Infinity: The Ekman Boundary Layer Problem
Rotating Navier-Stokes Equations in $${\mathbb R}^{3}_{+}$$ with Initial Data Nondecreasing at Infinity: The Ekman Boundary Layer Problem
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DOI：
10.1007/s00205-007-0053-9
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发表时间：
2004-11
影响因子：
2.5
通讯作者：
Y. Giga;K. Inui;A. Mahalov;Shin’ya Matsui;J. Saal
中科院分区：
文献类型：
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作者：
Y. Giga;K. Inui;A. Mahalov;Shin’ya Matsui;J. Saal
我们证明了时间局部存在性和唯一性的解决方案的边界层问题的旋转框架周围的固定解决方案称为埃克曼螺旋。我们在向量值齐次Besov空间中选择初始数据，其中2 <p< ∞。这里的Lp-可积性是在法向上施加的，而我们可能在切向分量上没有衰减，因为Besov空间包含非衰减函数，如概周期函数。一个关键的成分是向量值齐次Besov空间的理论。例如，我们为一般Banach空间提供并应用拉普拉斯算子的算子值有界H ∞-演算。
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 spacefor 2 <p< ∞. Here theLp-integrability is imposed in the normal direction, while we may have no decay in tangential components, since the Besov spacecontains 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 boundedH∞-calculus for the Laplacian infor a general Banach space.