Convergence towards self-similar asymptotic behavior for the dissipative quasi-geostrophic equations

• Autorzy: José A. Carrillo , Lucas C. F. Ferreira
• Języki publikacji: EN

Abstrakty

EN

This work proves the convergence in L¹(ℝ²) towards an Oseen vortex-like solution to the dissipative quasi-geostrophic equations for several sets of initial data with suitable decay at infinity. The relative entropy method applies in a direct way for solving this question in the case of signed initial data and the difficulty lies in showing the existence of unique global solutions for the class of initial data for which all properties needed in the entropy approach are met. However, the estimates obtained for the constructed global solutions in L¹ ∩ L² show the asymptotic simplification of the solutions even for unsigned initial data emphasizing the character of this equation to behave linearly for large times.

Kategorie tematyczne

• 35B40: Asymptotic behavior of solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2006
• Tom: 74
• Numer: 1
• Strony: 95-115

Daty

wydano

2006

Twórcy

autor

José A. Carrillo

• ICREA (Institució Catalana de Recerca i Estudis Avançats), and Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain

autor

Lucas C. F. Ferreira

• Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain

Identyfikatory

DOI

10.4064/bc74-0-5