Global Existence in Critical Spaces¶for Flows of Compressible¶Viscous and Heat-Conductive Gases

By Raphaël Danchin. 2001

215 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3f9f3119e81ca66430913b130024c84540e2c4c3

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In Applied Mathematics

In Control and Systems Engineering

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Citations in the corpus

Compressible Flow in a Half-Space with Navier Boundary Conditions (2005, result): “The solutions that we obtain may exhibit discontinuities in density and velocity gradient across hypersurfaces in Ω and are consequently much less regular and much more general than those of the small-smooth theories of Matsumura–Nishida [11] and Danchin [5].”
A Beale–Kato–Majda Criterion for Three Dimensional Compressible Viscous Heat-Conductive Flows (2011, background): “Thanks to Proposition 3 and (27), we have by Sobolev’s inequality that ‖u‖L∞(0,T ;H1( )) + ‖u‖L2(0,T ;W 1,q ( )) C, (33) for any q ∈ [2, 6], and the constant C depends on T, M and ‖u0‖H1( ).”
On the uniqueness in critical spaces for compressible Navier-Stokes equations (2005, methodology): “In [5] and [6], we investigated the following polytropic model for compressible heat conductive fluids:  ∂tρ + div(ρu) = 0, ∂t(ρu) + div(ρu ⊗ u) − div τ + ∇P = ρf, ∂t(ρ( |u|2 2 + e)) + div [u(ρ( |u|2 2 + e) + P )] = div(τ ·u) − div q + ρf · u.”
Existence results for viscous polytropic fluids with vacuum (2006, background): “We refer the readers to the papers [5, 6, 12, 18, 19, 20, 28, 29, 32] for some local or global results.”
Low Mach Number Limit of the Full Navier-Stokes Equations (2005, background): “The latter problem has been widely studied, starting from [29] and culminating in [6, 7] which investigate global strong solutions in spaces invariant by the scaling (1.”
Global Existence for the Multi-Dimensional Compressible Viscoelastic flows (2010, methodology): “Let us recall that using hybrid Besov spaces has been crucial for proving global well-posedness for compressible gases in critical spaces (see [4, 5]).”