Dissipative solutions of scaled compressible rotating Euler equations converge to strong solutions of a 2D horizontal incompressible Euler system in an infinite slab as Mach and Rossby numbers vanish proportionally to ε.
Generalized solutions to models of inviscid fluids
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abstract
We discuss several approaches to generalized solutions of problems describing the motion of inviscid fluids. We propose a new concept of dissipative solution to the compressible Euler system based on a careful analysis of possible oscillations and/or concentrations in the associated generating sequence. Unlike the conventional measure-valued solutions or rather their expected values, the dissipative solutions comply with a natural compatibility condition - they are classical solutions as long as they enjoy certain degree of smoothness.
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math.AP 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Singular limits for compressible inviscid rotating fluids
Dissipative solutions of scaled compressible rotating Euler equations converge to strong solutions of a 2D horizontal incompressible Euler system in an infinite slab as Mach and Rossby numbers vanish proportionally to ε.