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Global Existence and Exponential Decay to Equilibrium for DLSS-Type Equations

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Abstract

In this paper, we deal with two logarithmic fourth order differential equations: the extended one-dimensional DLSS equation and its multi-dimensional analog. We show the global existence of solution in critical spaces, its convergence to equilibrium and the gain of spatial analyticity for these two equations in a unified way.

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Acknowledgements

H. Bae was supported by NRF-2018R1D1A1B07049015. Part of this research was conducted while R. Granero-Belinchón was visiting UNIST funded by NRF-2018R1D1A1B07049015.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan, Republic of Korea

    Hantaek Bae

  2. Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Santander, Spain

    Rafael Granero-Belinchón

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  1. Hantaek Bae
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  2. Rafael Granero-Belinchón
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Correspondence to Rafael Granero-Belinchón.

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Bae, H., Granero-Belinchón, R. Global Existence and Exponential Decay to Equilibrium for DLSS-Type Equations. J Dyn Diff Equat 33, 1135–1151 (2021). https://doi.org/10.1007/s10884-020-09852-5

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  • DOI: https://doi.org/10.1007/s10884-020-09852-5

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