The restriction problem on the ellipsoid

Chan, Chi Hin; Czubak, Magdalena; Yoneda, Tsuyoshi

doi:10.1016/j.jmaa.2023.127358

Journal of Mathematical Analysis and Applications

2023

DOI: 10.1016/j.jmaa.2023.127358

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The restriction problem on the ellipsoid

Chi Hin Chan

Magdalena Czubak

Tsuyoshi Yoneda

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2024

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Recent developments in mathematical aspects of relativistic fluids

Disconzi

2024

Living Rev Relativ

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We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent fields, as well as to researches working on broader aspects of relativistic fluid dynamics interested in its mathematical formalism. Instead of complete proofs, which can be found in the published literature, here we focus on the proofs’ main ideas and key concepts. After an introduction to the relativistic Euler equations, we cover the following topics: a new wave-transport formulation of the relativistic Euler equations tailored to applications; the problem of shock formation for relativistic Euler; rough (i.e., low-regularity) solutions to the relativistic Euler equations; the relativistic Euler equations with a physical vacuum boundary; relativistic fluids with viscosity. We finish with a discussion of open problems and future directions of research.

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Recent developments in mathematical aspects of relativistic fluids

Disconzi

2024

Living Rev Relativ

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show abstract

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The restriction problem on the ellipsoid

Cited by 1 publication

References 20 publications

Recent developments in mathematical aspects of relativistic fluids

Recent developments in mathematical aspects of relativistic fluids

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