Investigation of a mathematical model from the theory of viscous fluids

This study is devoted to a nonlinear third-order ordinary differential equation featuring movable singularities. Two principal research tasks are addressed. The first concerns establishing a theorem on the existence and uniqueness of the solution to the Cauchy problem in the vicinity of a movable singular point. To tackle this, an approximate analytical solution is constructed, and corresponding error estimates are derived. The theoretical findings are supported by numerical simulations. The second task focuses on deriving both pointwise and interval-based criteria that ensure the presence of a movable singularity. These results form the foundation for constructing an algorithm to detect the location of such singular points.