The Newton's problem assuming non-constant density of the fluid
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914557312630784 |
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| author | López, Rafael |
| author_facet | López, Rafael |
| contents | 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 $u'(r_M) = \frac{1}{\sqrt{3}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11641 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Newton's problem assuming non-constant density of the fluid López, Rafael Analysis of PDEs Differential Geometry 49Q10, 49K30, 52A15 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 $u'(r_M) = \frac{1}{\sqrt{3}}$. |
| title | The Newton's problem assuming non-constant density of the fluid |
| topic | Analysis of PDEs Differential Geometry 49Q10, 49K30, 52A15 |
| url | https://arxiv.org/abs/2605.11641 |