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|Type:||Artigo de periódico|
|Title:||Self-similar Solutions For Active Scalar Equations In Fourier–besov–morrey Spaces|
|Abstract:||We are concerned with a family of dissipative active scalar equation with velocity fields coupled via multiplier operators that can be of positive-order. We consider sub-critical values for the fractional diffusion and prove global well-posedness of solutions with small initial data belonging to a framework based on Fourier transform, namely Fourier–Besov–Morrey spaces. Since the smallness condition is with respect to the weak norm of this space, some initial data with large (formula presented)-norm can be considered. Self-similar solutions are obtained depending on the homogeneity of the initial data and couplings. Also, we show that solutions are asymptotically self-similar at infinity. Our results can be applied in a unified way for a number of active scalar PDEs like 1D models on dislocation dynamics in crystals, Burgers’ equation, 2D vorticity equation, 2D generalized SQG, 3D magneto-geostrophic equations, among others.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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