A family of dissipative active scalar equations with singular velocity and measure initial data

作者：Ferreira Lucas C F^*

来源：Computers & Mathematics with Applications, 2012, 64(10): 3292-3301.

DOI：10.1016/j.camwa.2012.01.074

• Generalized surface quasi-geostrophic equations
• Besov-Morrey spaces
• Well-posedness
• Self-similarity
• Asymptotic behavior

This paper considers a family of generalized active scalar equations, with fractional dissipation, whose velocity fields are more singular than Riesz transform. We prove global well-posedness results for small initial data belonging to Besov-Morrey spaces, which contain strongly singular functions and measures concentrated at points (Diracs) and on smooth curves. Self-similar solutions are obtained for initial data and coupling-velocity operator with correct homogeneities. We also show an asymptotic behavior result and obtain a class of asymptotically self-similar solutions.

• 出版日期2012-11