Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids
Abstract
Many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite. Using classical methods, the authors develop a general theory of such problems. This theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magnetofluid dynamics including new constructive local existence theorems for the timesingular limit equations. In particular, the authors give an entirely selfcontained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the Mach number becomes small. The theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures. Similar results are developed also for the compressible and incompressible NavierStokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero.
 Publication:

Communications in Pure Applied Mathematics
 Pub Date:
 July 1981
 Bibcode:
 1981CPAM...34..481K
 Keywords:

 Compressible Fluids;
 Flow Theory;
 Hyperbolic Systems;
 Incompressible Fluids;
 NavierStokes Equation;
 Nonlinear Systems;
 Singularity (Mathematics);
 Coefficients;
 Existence Theorems;
 Isentropic Processes;
 Mach Number;
 Fluid Mechanics and Heat Transfer