Work

The Newton’s problem assuming non-constant density of the fluid

Year: 2026

Type: article

Abstract: This paper investigates the Newton’s problem of minimal resistance for a body moving through a fluid whose density decreases exponentially with altitude. We prove the local existence and regularity of radial solutions u ( r ) satisfying the initial conditions u ( 0 ) = u ′ ( 0 ) = 0 using a fixed-point theorem. We show that the maximal domain of the solution is finite, [ 0 , r M ) , terminating at a critical slope u ′ ( r M ) = 1 3 .

Source: Applied Mathematics Letters

DOI: 10.1016/j.aml.2026.109901

Author: Rafael López

Institution: Universidad de Granada

Language: English

Topic: Fluid dynamics and aerodynamics studies

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,800

Funders: Ministerio de Economía y Competitividad, Ministerio de Ciencia e Innovación, European Regional Development Fund, Agencia Estatal de Investigación