Reduction of the Two-Dimensional Stationary Navier-Stokes Problem to a Sequence of Fredholm Integral Equations of the Second Kind.
NATIONAL AERONUATICS AND SPACE ADMINISTRATION MOFFETT FIELD CA AMES RESEARCH CENTER
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For more than the last 20 years there has been a concerted effort to solve the stationary Navier-Stokes equations however, this has only been successful for a few special cases of primarily academic interest. An alternative approach has been to solve the equations numerically, and then compare the results with experiment. On occasion, such comparisons are in good agreement. However, such results are of dubious value since one has no a-priori way of knowing the relevance of such results until they are explicitly compared against experiment. Therefore, it would seem reasonable to conclude that the present approaches to solving the Navier-Stokes equations are of limited value. Accordingly, it is the purpose of this paper to show that there does, indeed, exist an equivalent representation of the problem that has significant potential in solving such problems. This is due to the fact that this equivalent representation of the problem consists of a sequence of Fredholm Integral Equations of the second kind, and the solving of this type of problem is very well developed. In addition, for the problem in this form, there is an excellent chance to also determine explicit error estimates, since one would now be dealing with bounded linear operators, rather than unbounded. Author
- Numerical Mathematics