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Existence, uniqueness, and computation of solutions for mixed problems in compressible fluid flow. (English) Zbl 0777.35063

Initial-boundary value problems are considered for the one-dimensional Navier-Stokes equations for compressible flow on a finite interval. Convergence of finite difference schemes are proved for each of three different cases of initial and boundary data. For BV discontinuous initial data that is piecewise smooth the density is shown to remain discontinuous and a bound is given for the error of an approximate solution in a norm that dominates the sup-norm of the density. For \(H^ 1\) initial data a different error bound is given in the same norm.

MSC:

35Q35 PDEs in connection with fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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