Self-similar proles in Analysis of Fluids: a 1D model and the compressible Euler equations

• Autores: Gonzalo Cao Labora
• Localización: Reports@SCM: an electronic journal of the Societat Catalana de Matemàtiques, ISSN-e 2385-4227, Vol. 6, Nº. 1, 2021, págs. 35-47
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen
  • català

    Presentem dos nous resultats en anàlisi de fluids relacionats amb l’existència de singularitats fent servir perfils autosimilars i anàlisi d’estabilitat al voltant d’ells.

    El primer resultat és una nova prova de la formació de singularitats per l’equació d’Okamoto–Sakajo–Wunsch amb petit paràmetre fent ´us d’un perfil autosimilar aproximat. A la segona part trobem nous perfils autosimilars, radials i suaus, per a l’equació d’Euler compressible i isentròpica. Aquest és el primer perfil d’aquest tipus trobat pel cas de gasos monoatòmics.

  • English

    We present two new results in Analysis of Fluids involving the existence of singularities via self-similar profiles and stability analysis around them. The first result is a new proof of the formation of singularities for the Okamoto-Sakajo-Wunsch equation with small parameter, which is done via a stability analysis around an approximate self-similar profile.The second result consists on the finding of new smooth radial self-similar profiles developing singularities for the isentropic compressible Euler equations. This is the first proof of such profile for the monatomic gas case.

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