# reduced navier stokes in mathematica urgent help please

by 01af
Tags: mathematica, navier-stokes, urgent
 P: 1 ok I am modelling airflow in the upper airway for application i obstructive sleep apnoea, but I have hit a brick wall with mathematica. I have a system of 3 differential equations with boundary conditions, and I need to solve to find 3 unknown functions numerically so that they may be plotted in various graphs. The equations are as follows: D[a[x]*u[x], x] == 0, u[x] u'[x] == -p'[x], p[x] - 1 == 2 (1 - ((a[x])^(-3/2))) - 50 (a''[x]). with boundary conditions: u[0] == 0.1, a[0] == 1, a[10] == 1, p[10] == 1. so initially I tried to use NDSolve like so.. NDSolve[{D[a[x]*u[x], x] == 0, u[x] u'[x] == -p'[x], p[x] - 1 == 2 (1 - ((a[x])^(-3/2))) - 50 (a''[x]), u[0] == 0.1, a[0] == 1, a[10] == 1, p[10] == 1}, {a}, {x, 0, 10}] but mathematica does this: Power::infy: "Infinite expression 1/0.^(3/2) encountered. " Infinity::indet: Indeterminate expression 0. ComplexInfinity encountered. >> Infinity::indet: Indeterminate expression 0. ComplexInfinity encountered. >> General::stop: Further output of Infinity::indet will be suppressed during this calculation. >> NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0.. >>` which is super annoying, any pointers as to where I'm going wrong would be great. I'm not even sure if I should be using NDSolve so let me know what you think. thanks in advance a.

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