Existence results for viscous polytropic fluids with vacuum

285 citations recorded by the source corpus.

How researchers see this paper

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

Serrin-Type Blowup Criterion for Viscous, Compressible, and Heat Conducting Navier-Stokes and Magnetohydrodynamic Flows (2012, result): “First, the following existence and uniqueness of local strong solutions when the initial density may not be positive and may vanish in an open set can be proved in a similar way as in [4] (cf.”
On Blowup of Classical Solutions to the Compressible Navier-Stokes Equations (2013, background): “1) has been studied extensively in[2, 1, 5, 3, 6, 8, 7, 14, 15, 17, 18, 19, 20, 22, 10, 11, 12, 13, 16] and the references therein.”
A Beale–Kato–Majda Criterion for Three Dimensional Compressible Viscous Heat-Conductive Flows (2011, background): “It should be pointed out that an initial vacuum is allowed in [4], but a compatibility condition of the initial data is required.”
On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities (2006, background): “In fact, the following result is proved essentially in [ 3 ] and thus stated without a detailed proof.”
Global Classical and Weak Solutions to the Three-Dimensional Full Compressible Navier–Stokes System with Vacuum and Large Oscillations (2011, methodology): “Recently, for the case that the initial density need not be positive and may vanish in open sets, Cho-Kim [6] obtained the local existence and uniqueness of strong solutions.”