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Self-similar solutions for the fractional viscous Burgers equation in Marcinkiewicz spaces

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Abstract

The aim of this paper is to study the existence of self-similar solutions to the Cauchy problem for the viscous Burgers fractional equation with initial conditions in Marcinkiewcz spaces \(L^{(p,\infty )}\). In particular, we obtain the decay of the Mittag–Leffler family associated with the linear problem in Marcinkiewcz spaces and of its gradient.

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Acknowledgements

A. Viana is partially supported by CNPq under the Grant number 308080/2021-1.

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Authors and Affiliations

  1. IMECC, Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda, Campinas, São Paulo, 13083859, Brazil

    Edmundo Capelas de Oliveira & Maria Elismara de Sousa Lima

  2. Departmento de Matemática, Universidade Federal de Sergipe, Av. Marcelo Deda Chagas, São Cristóvão, Sergipe, 49107230, Brazil

    Arlúcio Viana

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  1. Edmundo Capelas de Oliveira
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de Oliveira, E.C., de Sousa Lima, M.E. & Viana, A. Self-similar solutions for the fractional viscous Burgers equation in Marcinkiewicz spaces. Comp. Appl. Math. 44, 94 (2025). https://doi.org/10.1007/s40314-024-03012-x

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