On the incompressible limit of the compressible Euler equation. (English) Zbl 0638.35012
The solution of the initial value problem for the compressible Euler equation tends to the solution of the corresponding incompressible Euler equation with the corresponding initial data, as the Mach number (which is proportional to a parameter 1/\(\lambda)\) tends to zero. Under suitable conditions, we also obtain the asymptotic expansion theorem for those solutions, when \(\lambda\) is large.
MSC:
| 35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 35L60 | First-order nonlinear hyperbolic equations |
| 35C20 | Asymptotic expansions of solutions to PDEs |
Keywords:
incompressible limit; initial value problem; compressible Euler equation; incompressible Euler equation; Mach number; asymptotic expansionReferences:
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