Anne Bronzi , Ricardo Guimarães , Cecilia Mondaini
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On the locally self-similar blowup for the generalized SQG equation
We analyze finite-time blowup scenarios of locally self-similar type for the inviscid generalized surface quasi-geostrophic equation (gSQG) in . Under an growth assumption on the self-similar profile and its gradient, we identify appropriate ranges of the self-similar parameter where the profile is either identically zero, and hence blowup cannot occur, or its asymptotic behavior can be characterized, for suitable . Our results extend the work by Xue [38] regarding the SQG equation, and also partially recover the results proved by Cannone and Xue [3] concerning globally self-similar solutions of the gSQG equation.
期刊介绍:
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics