Global well‐posedness of classical solutions with large oscillations and vacuum to the three‐dimensional isentropic compressible Navier‐Stokes equations
By Xiangdi Huang, Jing Li, Zhouping Xin. 2010
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We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible Navier‐Stokes equations in three spatial dimensions with smooth initial data that are of small energy but possibly large oscillations with constant state as far field, which could be either vacuum or nonvacuum. The initial density is allowed to vanish, and the spatial measure of the set of vacuum can be arbitrarily large; in particular, the initial density can even have compact support. These results generalize previous results on classical solutions for initial densities being strictly away from vacuum and are the first for global classical solutions that may have large oscillations and can contain vacuum states. © 2012 Wiley Periodicals, Inc.
Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/72edefe0eb459574e5599bfc052716c9a0148704
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In Applied Mathematics
In Computational Mechanics
In Mathematical Physics
Citations in the corpus
- On Blowup of Classical Solutions to the Compressible Navier-Stokes Equations (2013, background): “Despite the progress on various blow-up criterion [10,11,13], and the surprising results on global well-posedness of the classical solution to the 3-dimensional compressible Isentropic Navier-Stokes system for initial data with small total energy but possible large oscillations and containing vacuum”
- Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities (2015, background): “Recently, Huang-Li-Xin [16] obtained the global classical solutions with the density containing vacuum provided the initial energy is suitably small.”