We prove the global-in-time existence of weak solutions to the Navier–Stokes equations of compressible isentropic flow in three space dimensions with adiabatic exponent γ ≥ 1. Initial data and solutions are small in L 2 around a non-constant steady state with densities being positive and essentially bounded. No smallness assumption is imposed on the external forces when γ = 1. A great deal of information about partial regularity and large-time behavior is obtained. Copyright © 2012 Springer Basel AG.
CitationSuen, A. (2013). Global solutions of the Navier–Stokes equations for isentropic flow with large external potential force. Zeitschrift für angewandte Mathematik und Physik, 64(3), 767-784. doi: 10.1007/s00033-012-0263-3
- Navier–Stokes equations
- Compressible flow
- Global weak solutions