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

Applied Mathematics Letters 2026 Open access

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Authors: Rafael LOPEZ
DOI: 10.1016/j.aml.2026.109901
Cited by: 2
References: 2

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 .

Fields of Study & Subjects

Navier-Stokes equation solutions Nonlinear Partial Differential Equations Geometric Analysis and Curvature Flows

Publication details

Journal / source
Applied Mathematics Letters
Publisher
Elsevier BV
Volume
177
Pages
109901–109901
Publication date
24 February 2026
Language
EN