Abstract
We consider a family of dissipative active scalar equations outside the $L^{2}$-space. This was introduced in [7] and its velocity fields are coupled with the active scalar via a class of multiplier operators which morally behave as derivatives of positive order. We prove global well-posedness and time-decay of solutions, without smallness assumptions, for initial data belonging to the critical Lebesgue space $L^{\frac{n}{2\gamma-\beta}}(\mathbb{R}^{n})$ which is a class larger than that of the above reference. Symmetry properties of solutions are investigated depending on the symmetry of initial data and coupling operators.
Citation
Lucas C. F. Ferreira. Lidiane S. M. Lima. "Global well-posedness and symmetries for dissipative active scalar equations with positive-order couplings." Publ. Mat. 60 (2) 525 - 550, 2016. https://doi.org/10.5565/PUBLMAT_60216_08
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