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Construction of solutions for compressible, isentropic Navier-Stokes equations in one space dimension with nonsmooth initial data. (English) Zbl 0635.35074

The author gives a constructive approach to the global existence for the system of equations \[ v_ t-u_ x=0,\quad u_ t+p(v)_ x=(\epsilon (v)u_ x)_ x\quad for\quad x\in {\mathbb{R}},\quad t>0 \] with \(L^ 2\)- initial data (the initial v being also in BV). A weak solution is obtained as the limit of a finite-difference scheme (with discretization in space variable only) satisfying some heuristic jump condition. So the approximate solutions verify a system of ordinary differential equations together with the jump condition.
Reviewer: C.Popa

MSC:

35Q30 Navier-Stokes equations
35A35 Theoretical approximation in context of PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
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References:

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