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Abstract
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Here we develop a method for investigating global strong solutions of partially
dissipative hyperbolic systems in the critical regularity setting. Compared to
the recent works by Kawashima and Xu, we use
hybrid Besov spaces with
different regularity exponents in low and high frequencies. This allows us
to consider more general data and to track the exact dependency on the
dissipation parameter for the solution. Our approach enables us to go beyond the
framework in the treatment of the low frequencies of the solution, which is totally
new, to the best of our knowledge.
The focus is on the one-dimensional setting (the multidimensional case will be
considered in a forthcoming paper) and, for expository purposes, the first part of the
paper is devoted to a toy model that may be seen as a simplification of the compressible
Euler system with damping. More elaborate systems (including the compressible Euler
system with general increasing pressure law) are considered at the end of the paper.
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Keywords
hyperbolic systems, critical regularity, time decay,
partially dissipative
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Mathematical Subject Classification
Primary: 35Q35, 76N10
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Milestones
Received: 6 January 2021
Revised: 25 October 2021
Accepted: 5 January 2022
Published: 29 April 2022
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