## 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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