Related papers: Nash embedding, shape operator and Navier-Stokes e…

Based on Leray's formulation of the Navier-Stokes equations and the conditions of the exact linear representation of the nonlinear problem found in this paper, a compact explicit expression for the exact operator solution of the…

Many shape analysis methods treat the geometry of an object as a metric space that can be captured by the Laplace-Beltrami operator. In this paper, we propose to adapt the classical Hamiltonian operator from quantum mechanics to the field…

We investigate in the present paper the Navier-Stokes equations on quantum Euclidean spaces $\mathbb{R}^d_{\theta}$ with $\theta$ being a $d\times d$ antisymmetric matrix, which is a standard example of non-compact noncommutative manifolds.…

We show that non-uniqueness of the Leray-Hopf solutions of the Navier--Stokes equation on the hyperbolic plane observed in arXiv:1006.2819 is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on the…

Motivated by Nash equilibrium problems on 'curved' strategy sets, the concept of Nash-Stampacchia equilibrium points is introduced via variational inequalities on Riemannian manifolds. Characterizations, existence, and stability of…

In this article, we construct stationary solutions to the Navier-Stokes equations on certain Riemannian $3$-manifolds that exhibit Turing completeness, in the sense that they are capable of performing universal computation. This…

The relationship between Koopman mode decomposition, resolvent mode decomposition and exact invariant solutions of the Navier-Stokes equations is clarified. The correspondence rests upon the invariance of the system operators under symmetry…

Let $M$ be a complete Riemannian manifold satisfying a weighted Poincar\'e inequality, and let $\mathcal{E}$ be a Hermitian vector bundle over $M$ equipped with a metric covariant derivative $\nabla$. We consider the operator…

We prove that the Navier-Stokes, the Euler and the Stokes equations admit a Lagrangian structure using the stochastic embedding of Lagrangian systems. These equations coincide with extremals of an explicit stochastic Lagrangian functional,…

We consider the motion of an incompressible viscous fluid on a compact Riemannian manifold $\sM$ with boundary. The motion on $\sM$ is modeled by the incompressible Navier-Stokes equations, and the fluid is subject to pure or partial slip…

We study Laplace-type operators on hybrid manifolds, i.e. on configurations consisting of closed two-dimensional manifolds and one-dimensional segments. Such an operator can be constructed by using the Laplace-Beltrami operators on each…

We analyze the incompressible Navier-Stokes equations on a class of non-compact Riemannian manifolds within the framework of Morrey spaces. Assuming bounded geometry together with negative Ricci and sectional curvature (e.g., hyperbolic…

In this paper, the strong formulation of the generalised Navier-Stokes momentum equation is investigated. Specifically, the formulation of shear-stress divergence is investigated, due to its effect on the performance and accuracy of…

A Navier--Stokes system on a curve is discussed. The quotient equation for this system is found. The quotient is used to find some solutions of Navier--Stokes system. Using virial expansion of the Planck potential, we reduce the quotient…

We consider the inverse problem of determining a compact Riemannian manifold with boundary from fixed time observations of the solution, restricted to a small subset in space, for the Navier-Stokes system with a local source on the…

Let $M^n$ be a compact orientable smooth Riemannian submanifold of dimension $n\geq 3$ in $\mathbb R^d$. We construct a family of deformed Hodge Laplacians $\Delta_t^*$, $t>0$, acting on differential forms and defined through the extrinsic…

WE PRESENT THE RANDOM REPRESENTATIONS FOR THE NAVIER-STOKES VORTICITY EQUATIONS FOR AN INCOMPRESSIBLE FLUID IN A SMOOTH MANIFOLD WITH BOUNDARY AND REFLECTING BOUNDARY CONDITIONS FOR THE VORTICITY. WE SPECIALIZE OUR CONSTRUCTIONS TO…

We derive a numerical approximation of the Laplace-Beltrami operator on compact surfaces embedded in $\mathbb{R}^3$ with an axial symmetry. To do so we use a noncommutative Laplace operator defined on the space of finite dimensional…

This paper is concerned with the construction of discrete counterparts of the Laplace-Beltrami operator on Riemannian manifolds that can be effectively used in the numerical solution of partial differential equations. Since existing…

This work presents an approach to the Navier-Stokes equations that is phrased in unbiased Eulerian coordinates, yet describes objects that have Lagrangian significance: particle paths, their dispersion and diffusion. The commutator between…