On the p-adic Navier–Stokes equation

ABSTRACT

We prove the local solvability of the p-adic analog of the Navier–Stokes equation. This equation describes, within the p-adic model of porous medium, the flow of a fluid in capillaries.

COMMUNICATED BY:

• Alexander Pankov

KEYWORDS:

• p-adic numbers
• Vladimirov's p-adic fractional differentiation operator
• p-adic model of porous medium
• Navier–Stokes equation

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• Primary: 35S10
• Secondary: 11S80
• 76S05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The second author is grateful to Mathematical Institute, Linnaeus University, for hospitality during his visits to Växjö. The work of the second author was also supported in part by Grant 23/16-18 ‘Statistical dynamics, generalized Fokker-Planck equations, and their applications in the theory of complex systems’ of the Ministry of Education and Science of Ukraine.