On the Existence of Globally Defined Weak Solutions to the Navier—Stokes Equations

By Eduard Feireisl, Antonín Novotný, Hana Petzeltová. 2001

921 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/6758cfbdb0f7e4db41929d96d7f5d3d5e3f35eb9

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

The Convergence of the Navier–Stokes–Poisson System to the Incompressible Euler Equations (2006, result): “The proof is completely similar to those of Lions (1998), Feireisl et al. (2001), Feireisl (2001), and Ducomet et al. (2001).”
Existence of global weak solutions for 3D degenerate compressible Navier–Stokes equations (2015, background): “To remove the difficulty from the vacuum, Lions in [24] introduced the concept of renormalized solutions to establish the global existence of weak solutions for γ > 9 5 concerning large initial data that may vanish, and then FeireislNovotný-Petzeltová [11] and Feireisl [12] extended the existence re”
Weak–Strong Uniqueness for the Isentropic Compressible Navier–Stokes System (2008, neutral): “[7] to γ > d2 .”
Global Classical and Weak Solutions to the Three-Dimensional Full Compressible Navier–Stokes System with Vacuum and Large Oscillations (2011, background): “[7] E. Feireisl, Dynamics of Viscous Compressible Fluids, Oxford Science Publication, Oxford, 2004.”
Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities (2015, background): “2) with γ ∈ (1, 2] for general initial data, which is in sharp contrast to the case that h and g are both constants, where the condition γ > 3/2 is essential in the analysis of Lions [26] and Feireisl-Novotny-Petzeltová [8].”
Vanishing of Vacuum States and Blow-up Phenomena of the Compressible Navier-Stokes Equations (2008, background): “For instance, the one-dimensional (1D) problems were addressed by Kazhikhov et al [24] for sufficiently smooth data, and by Serre [46,47] and Hoff [18] for discontinuous initial data, where the data are uniformly away from the vacuum; the multidimensional problems (1.1) were investigated by Matsumur”
On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities (2006, background): “Then Lions’ theory has been improved by several authors to deduce more general results; see [7, 8, 9, 10, 14, 15] for details.”
On the Inviscid Limit for the Compressible Navier–Stokes System in an Impermeable Bounded Domain (2012, positive): “In this setting the existence of global weak solutions of the Navier-Stokes equations is known since the pioneering work [33] of Lions, later improved by Feireisl, Novotný and Petzeltová in [10], see also [11, 12], for various boundary conditions.”
Existence results for viscous polytropic fluids with vacuum (2006, neutral): “For details, refer to [1, 3, 7, 10, 15, 17, 22].”
On the Barotropic Compressible Navier–Stokes Equations (2007, background): “( 2001 ), and recently by Feireisl for variational solutions of the full system of the Navier–Stokes equations with viscosity coefficients depending on the temperature (Feireisl, 2004 ).”