Global Classical and Weak Solutions to the Three-Dimensional Full Compressible Navier–Stokes System with Vacuum and Large Oscillations

By Xiangdi Huang, Jing Li. 2011

163 citations recorded by the source corpus.

For the three-dimensional full compressible Navier–Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid, we establish the global existence and uniqueness of classical solutions with smooth initial data which are of small energy but possibly large oscillations where the initial density is allowed to vanish. Moreover, for the initial data, which may be discontinuous and contain vacuum states, we also obtain the global existence of weak solutions. These results generalize previous ones on classical and weak solutions for initial density being strictly away from a vacuum, and are the first for global classical and weak solutions which may have large oscillations and can contain vacuum states.

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

View Paper: https://www.semanticscholar.org/paper/7b713a4bccc9adf89618d6581c3a32bebf32a5ea

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In Applied Mathematics

1. Xiangdi Huang
2. Jing Li
3. Zhouping Xin

In Control and Systems Engineering

1. Xiangdi Huang
2. Jing Li

In Mathematical Physics

1. Xiangdi Huang
2. Jing Li
3. Zhouping Xin

Citations in the corpus

• Serrin-Type Blowup Criterion for Viscous, Compressible, and Heat Conducting Navier-Stokes and Magnetohydrodynamic Flows (2012, result): “42), whose proofs are similar to those in [15,40] and can be found in Appendix A:”