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Life span and global existence of 2-D compressible fluids. (English) Zbl 0997.35052
Salvi, Rodolfo (ed.), The Navier-Stokes equations: theory and numerical methods. Proceedings of the international conference, Varenna, Lecco, Italy, 2000. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 223, 99-111 (2002).
The paper deals with the existence and uniqueness of smooth (classical) solutions for a barotropic inviscid compressible fluid in the halfplane. The aim is to solve the corresponding initial-boundary value problem on the time interval $$[0,T]$$, where $$T>0$$ is arbitrary, for “almost” constant initial densities. To this end the solution is represented as the sum of irrotational flow, incompressible flow and the remainder due to the nonlinear interaction.
For the entire collection see [Zbl 0972.00046].

MSC:
 35Q35 PDEs in connection with fluid mechanics 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 76J20 Supersonic flows