Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 1999 · 194 citations · 11 references
Natural SciencesPhysicsAerodynamicsFluid DynamicsFluid MechanicsCompressible FlowIncompressible FlowInviscid FlowNavier-stokes EquationsViscous FlowWeak FormulationCompressible Navier-stokes EquationsCompressible Viscous FlowConvergenceIncompressible Navier-stokes EquationsIncompressible Viscous FlowMach NumberVelocityWeak Solutions
This paper is devoted to the low Mach number limit of weak solutions to the com-pressible Navier{Stokes equations for isentropic fluids in the whole space Rd (d = 2 or 3). This problem was investigated by P. L. Lions and N. Masmoudi. We present here a dierent approach based upon Strichartz’s estimates for the linear wave equa-tion in the inviscid case, which improves the convergence result and simplies the proof. We prove that the velocity eld is strongly compact and converges to a global weak solution of the incompressible Navier{Stokes equations.
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M. Keel, Terence Tao · American Journal of Mathematics · 1998 · 2.1K citations
Fast Singular Limits of Hyperbolic PDEs
Steven Schochet · Journal of Differential Equations · 1994 · 354 citations