Abstract. We study the existence and uniqueness of regular solutions to the Navier–Stokes initial-boundary value problem with non-decaying bounded initial data, in a smooth exterior domain of Rn, n ≥ 3. The pressure field, p, associated to these solutions may grow, for large |x|, as O(|x|γ), for some γ ∈ (0, 1). Our class of existence is sharp for well posedeness, in that we show that uniqueness fails if p has a linear growth at infinity. We also provide a sufficient condition on the spatial growth of ∇p for the boundedness of v, at all times. Also this latter result is shown to be sharp.
On the Navier–Stokes Problem in Exterior Domains with Non Decaying Initial Data
MAREMONTI, Paolo;
2012
Abstract
Abstract. We study the existence and uniqueness of regular solutions to the Navier–Stokes initial-boundary value problem with non-decaying bounded initial data, in a smooth exterior domain of Rn, n ≥ 3. The pressure field, p, associated to these solutions may grow, for large |x|, as O(|x|γ), for some γ ∈ (0, 1). Our class of existence is sharp for well posedeness, in that we show that uniqueness fails if p has a linear growth at infinity. We also provide a sufficient condition on the spatial growth of ∇p for the boundedness of v, at all times. Also this latter result is shown to be sharp.File in questo prodotto:
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