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The Navier–Stokes flow around the linearly growing steady state with bounded disturbance

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Abstract

The existence and uniqueness of locally-in-time solutions of the Cauchy problem to the incompressible Navier–Stokes equations is established. The initial velocity U 0 is of the form U 0(x) := u 0(x)−M x, where M is a real-valued matrix and u 0 is a bounded smooth function. Our solutions satisfy the equations in the classical sense, even though the semigroup is not analytic. If M is skew-symmetric, and u 0 is small and a sum of trigonometric functions, then obtained solutions can be extended globally-in-time with the exponential decay in time.

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  1. Fachbereich Mathematik, Arbeitsgruppe Angewandte Analysis, Technische Universität Darmstadt, Darmstadt, Germany

    Okihiro Sawada

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  1. Okihiro Sawada
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Correspondence to Okihiro Sawada.

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Sawada, O. The Navier–Stokes flow around the linearly growing steady state with bounded disturbance. Ann. Univ. Ferrara 55, 367–376 (2009). https://doi.org/10.1007/s11565-009-0078-0

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  • DOI: https://doi.org/10.1007/s11565-009-0078-0

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