Mathematical Foundations of Fluid Mechanics
A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".
Deadline for manuscript submissions: 31 July 2026 | Viewed by 182
Special Issue Editor
2. Mathematics Section, Thames Valley District School Board, London, ON N5W 5P2, Canada
Interests: fluid dynamics; PDE; turbulence theory; numerical analysis of PDE
Special Issue Information
Dear Colleagues,
A wide spectrum of mathematical models, problems, methods and techniques are used in modern fluid dynamics. This Special Issue welcomes the following topics in mathematical foundations of fluid mechanics. It contains the derivation of the fundamental equations of fluid flow and presents the formulation of mathematical models and boundary value problems describing a number of flows important in pure and applied research. Particular attention is paid to the investigation of qualitative properties of models and to their numerical solution. In particular, the existence and uniqueness of the solution to incompressible and compressible inviscid as well as viscous flow is studied using the theory of complex functions, integral equations, and partial differential equations, including the concepts of weak and measure-valued solutions. Furthermore, theoretical analyses and practical implementations of basic methods of computational fluid dynamics, i.e., finite difference, finite element, and finite volume methods are presented. The treatment is accompanied by a number of examples of computed flow fields.
Harmonic analysis methods are welcome as solutions to the Navier–Stokes problem.
The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize Problems—remains an important open challenge in partial differential equations (PDEs) research despite substantial studies on turbulence and three-dimensional fluids. This Special Issue will cover the role of harmonic analysis in the PDEs of fluid mechanics.
Also this Special Issue will focus on incompressible deterministic Navier–Stokes equations in the case of a fluid filling the whole space. It will explore the meaning of the equations, open problems, and recent progress. It includes classical results on local existence and studies criterion for regularity or uniqueness of solutions. The Issue will incorporate recent references that highlight active mathematical research in the field.
This Special Issue will cover a balance between the derivations of equations and models, the theory of boundary value problems of fluid dynamics and numerical methods. Accompanied by examples, research articles in it will fill the gap between the engineering literature and highly specialized mathematical monographs in a mathematically precise but accessible way.
We look forward to receiving your valuable contributions.
Dr. Terry E. Moschandreou
Guest Editor
Manuscript Submission Information
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Keywords
- Navier–Stokes equation
- potential
- fluid mechanics
- rotation
- vorticity
- inverse problems
- fluid and aerodynamics
- existence theory
- blowup
- viscosity
- inviscid flow
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