Improperly Posed Problem

Improperly posed problem may lead to

1. Infinite many solutions
2. No solution
3. Finite number of solutions

Specified enough equations for the number of unknowns but no boundary or initial conditions may leads to infinite number of solutions on the other hand over specified boundary conditions or initial conditions will lead to no solution. If the number of initial or boundary condition is not complete then that may lead to a finite number of solutions. An example of this is the heated below flow. When heated below fluid has negative density gradient in y direction. If x side boundary condition are not specified we may have the following solutions.

Another example: Free convection between two vertical plates. Governing equations are properly given, if Boundary conditions on y is missing then

(a) gas :has net flow (b) gas has zero flow.