Non-stationary Navier–Stokes equations in 2D power cusp domain II. Existence of the solution
| Autor: | Alicija Raciene, Konstantin Pileckas |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
010101 applied mathematics
Cusp (singularity) Physics Nonstationary Navier-Stokes problem power cusp domain singular solutions asymptotic expansion 010102 general mathematics Mathematical analysis 0101 mathematics Navier–Stokes equations Asymptotic expansion 01 natural sciences Analysis Domain (mathematical analysis) Power (physics) |
| Zdroj: | Advances in nonlinear analysis, Berlin : Walter de Gruyter GmbH, 2021, vol. 10, iss. 1, p. 1011-1038 |
| ISSN: | 2191-9496 2191-950X |
| Popis: | The initial boundary value problem for the non-stationary Navier-Stokes equations is studied in 2D bounded domain with a power cusp singular point O on the boundary. We consider the case where the boundary value has a nonzero flux over the boundary. In this case there is a source/sink in O and the solution necessary has infinite energy integral. In the first part of the paper the formal asymptotic expansion of the solution near the singular point was constructed. In this, second part, the constructed asymptotic decomposition is justified, i.e., existence of the solution which is represented as the sum of the constructed asymptotic expansion and a term with finite energy norm is proved. Moreover, it is proved that the solution represented in this form is unique. |
| Databáze: | OpenAIRE |
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