Self-similar solutions of stationary Navier–Stokes equations
| Autor: | Zuoshunhua Shi |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Momentum flux
Applied Mathematics 010102 general mathematics Mathematical analysis Rotational symmetry Invariant (physics) Non-dimensionalization and scaling of the Navier–Stokes equations 01 natural sciences Physics::Fluid Dynamics 010101 applied mathematics Arbitrarily large 0101 mathematics Navier–Stokes equations Scaling Analysis Real number Mathematics |
| Zdroj: | Journal of Differential Equations. 264:1550-1580 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2017.10.002 |
| Popis: | In this paper, we mainly study the existence of self-similar solutions of stationary Navier–Stokes equations for dimension n = 3 , 4 . For n = 3 , if the external force is axisymmetric, scaling invariant, C 1 , α continuous away from the origin and small enough on the sphere S 2 , we shall prove that there exists a family of axisymmetric self-similar solutions which can be arbitrarily large in the class C l o c 3 , α ( R 3 \ 0 ) . Moreover, for axisymmetric external forces without swirl, corresponding to this family, the momentum flux of the flow along the symmetry axis can take any real number. However, there are no regular ( U ∈ C l o c 3 , α ( R 3 \ 0 ) ) axisymmetric self-similar solutions provided that the external force is a large multiple of some scaling invariant axisymmetric F which cannot be driven by a potential. In the case of dimension 4, there always exists at least one self-similar solution to the stationary Navier–Stokes equations with any scaling invariant external force in L 4 / 3 , ∞ ( R 4 ) . |
| Databáze: | OpenAIRE |
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