Well-posedness of 3-D inhomogeneous Navier–Stokes equations with highly oscillatory initial velocity field
| Autor: | Guilong Gui, Ping Zhang, Hammadi Abidi |
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| Rok vydání: | 2013 |
| Předmět: |
Applied Mathematics
General Mathematics Mathematical analysis Hagen–Poiseuille flow from the Navier–Stokes equations Mathematics::Analysis of PDEs Compressibility Probability density function Vector field Non-dimensionalization and scaling of the Navier–Stokes equations Navier–Stokes equations Upper and lower bounds Well posedness Mathematics |
| Zdroj: | Journal de Mathématiques Pures et Appliquées. 100:166-203 |
| ISSN: | 0021-7824 |
| DOI: | 10.1016/j.matpur.2012.10.015 |
| Popis: | Without smallness assumption on the variation of the initial density function, we first prove the local well-posedness of 3-D incompressible inhomogeneous Navier–Stokes equations with initial data ( a 0 , u 0 ) in the critical Besov spaces B λ , 1 3 λ ( R 3 ) × B ˙ p , 1 3 p − 1 ( R 3 ) for λ , p given by Theorem 1.1. Then we prove this system is globally well-posed provided that ‖ u 0 ‖ B ˙ p , 1 3 p − 1 is sufficiently small. In particular, this result implies the global well-posedness of 3-D inhomogeneous Navier–Stokes equations with highly oscillatory initial velocity field and any initial density function with a positive lower bound. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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