Special Session 27: Recent Trends in Navier-Stokes Equations, Euler Equations, and Related Problems
Local-in-time existence of strong solutions to a class of the compressible non-Newtonian Navier-Stokes equations
Vaclav Macha
Institute of Mathematics of the Czech Academy of Sciences Czech Rep
Co-Author(s): Martin Kalousek and \v{S}\`{a}rka Ne\v{c}asov\`{a}
Abstract:
We show the local-in-time existence of a strong solution to the generalized compressible Navier-Stokes equations for arbitrarily large initial data. The goal is reached by $L^p$-theory for linearized equations which are obtained with help of the Weis multiplier theorem and can be seen as a generalization of the work of Shibata and Enomoto (devoted to compressible fluids) to compressible non-Newtonian fluids.