LOCAL THEORY IN CRITICAL SPACES FOR COMPRESSIBLE VISCOUS AND HEAT-CONDUCTIVE GASES

By Raphaël Danchin. 2001

293 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/a3ada13bde7cbfc62ee2b84ab634b84f05196162

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Dissipative Quasi-Geostrophic Equation for Large Initial Data in the Critical Sobolev Space (2006, background): “If the equation has a class of scaling invariance, then it coincides with the most suitable space to construct the solution which is expected unique and regular. (See, e.g. Danchin [ 7 ], Koch-Tataru [11].)”
On a maximum principle and its application to logarithmically critical Boussinesq system (2009, result): “Next we recall the following result, proved in [Chen et al. 2007; Danchin 2001; Planchon 2000].”
The generalized incompressible Navier-Stokes equations in Besov spaces (2004, methodology): “Besov spaces include many of the frequently-used function spaces such as the Sobolev spaces and the Hölder spaces and constitute a very natural setting for studying solutions of various partial differential equations ([1],[4],[5],[7],[12],[13],[15]).”
ON THE ILL-POSEDNESS OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS (2011, methodology): “Motived by Fujita-Kato’s result [12] on the incompressible Navier-Stokes equations, Danchin studied in a series of papers [7, 8, 9] the well-posedness for the compressible Navier-Stokes equations in the critical spaces.”
Well-Posedness in Critical Spaces for Barotropic Viscous Fluids with Truly Not Constant Density (2007, methodology): “Now, according to Theorem 4.2 in Danchin (2001), one can solve ÑSC with the smooth data an0 u n 0 f n .”
Global existence in critical spaces for compressible Navier-Stokes equations (2000, background): “The generalization of this latter result to other functional spaces and to heat-conductive gases will be the object of a forthcoming article (see [ 9 ]).”
Existence results for viscous polytropic fluids with vacuum (2006, methodology): “We refer the readers to the papers [ 5 , 6, 12, 18, 19, 20, 28, 29, 32] for some local or global results.”
Existence of Global Strong Solutions in Critical Spaces for Barotropic Viscous Fluids (2010, background): “As similar arguments have been employed in [12] or [16], we only give the outlines of the proof.”
Equation de Navier-Stokes avec densité et viscosité variables dans l'espace critique (2007, unknown): “Rappelons tout d’abord une inégalité semblable à l’inégalité de Bernstein (voir [10]) qui nous permet de gagner deux dérivées à partir du laplacien dans L si 1 < p < ∞.”
Global solutions to 2-d inhomogeneous navier-stokes system with general velocity (2012, unknown): “5 of [7] that −∆∆jvλ̄ | |∆jvλ̄|∆jvλ̄ ) ≥ c̄2‖∆jvλ̄‖pLp for some positive constant c̄, from which and (4.”
Global solutions to the 3-D incompressible inhomogeneous Navier–Stokes system (2012, methodology): “Applying the operator j to the above equation and taking the L2 inner product of the resulting equation with | ju λ| ju λ (again in the case when p ∈ (1,2), we need to make some modification as that [9]), we obtain”
A Global Existence Result for the Compressible Navier–Stokes Equations in the Critical Lp Framework (2010, background): “In the case 2 ≤ p 1 ≤ d, the uniqueness in E sp 1 ,r ( T ) for System (2) has been established in [8, 9].”
Global Classical Solutions for Partially Dissipative Hyperbolic System of Balance Laws (2012, background): “[2, 11, 35]) whereas the time exponent θ behaves according to Hölder inequality.”
On the uniqueness in critical spaces for compressible Navier-Stokes equations (2005, methodology): “[5]) then yield uniqueness on the whole interval [0, T ).”