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Instability of equatorial edge waves in the background flow. (English) Zbl 1355.35182

The purpose of this paper is to find two a priori estimates of the finite Dirichlet integral for a homogeneous stationary Navier-Stokes equation \[ \begin{cases} -\Delta v+(v\cdot \nabla)v+ \nabla p=0\text{ in }\mathbb{R}^3, \\ \operatorname{div} v=0 \text{ in }\mathbb{R}^3. \end{cases} \] The proofs use Lorentz spaces, Hölder inequality, Biot-Savart law, Liouville theorem for harmonic functions, integration by parts, Riesz transform, Marcinkiewicz interpolation theorem.

MSC:

35Q86 PDEs in connection with geophysics
76E20 Stability and instability of geophysical and astrophysical flows
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
76B70 Stratification effects in inviscid fluids
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