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2016 Global well-posedness and symmetries for dissipative active scalar equations with positive-order couplings
Lucas C. F. Ferreira, Lidiane S. M. Lima
Publ. Mat. 60(2): 525-550 (2016). DOI: 10.5565/PUBLMAT_60216_08

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.

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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

Information

Received: 2 December 2014; Published: 2016
First available in Project Euclid: 11 July 2016

zbMATH: 1348.35185
MathSciNet: MR3521499
Digital Object Identifier: 10.5565/PUBLMAT_60216_08

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Rights: Copyright © 2016 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.60 • No. 2 • 2016
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