Self-similar solutions in weak \(L^ p\)-spaces of the Navier-Stokes equations (Q1923684)
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scientific article; zbMATH DE number 933289
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Self-similar solutions in weak \(L^ p\)-spaces of the Navier-Stokes equations |
scientific article; zbMATH DE number 933289 |
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Self-similar solutions in weak \(L^ p\)-spaces of the Navier-Stokes equations (English)
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21 April 1997
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Summary: The most important result stated in this paper is a theorem on the existence of global solutions for the Navier-Stokes equations in \(\mathbb{R}^n\) when the initial velocity belongs to the space weak \(L^n (\mathbb{R}^n)\) with a sufficiently small norm. Furthermore, this fact leads us to obtain self-similar solutions if the initial velocity is, besides, a homogeneous function of degree \(-1\). Partial uniqueness is also discussed.
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existence
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global solutions
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Navier-Stokes equations
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self-similar solutions
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initial velocity
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uniqueness
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