Related papers: Incompressible Euler equations with stochastic for…
Stochastic factors are not negligible in applications of hydrostatic Euler equations (EE) and hydrostatic Navier-Stokes equations (NSE). Compared with the deterministic cases for which the ill-posedness of these models in the Sobolev spaces…
The existence of martingale solutions of the hydrodynamic-type equations in 3D possibly unbounded domains is proved. The construction of the solution is based on the Faedo-Galerkin approximation. To overcome the difficulty related to the…
We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the…
We present a geometric analysis of the incompressible averaged Euler equations for an ideal inviscid fluid. We show that solutions of these equations are geodesics on the volume-preserving diffeomorphism group of a new weak right invariant…
We consider the Euler equations on $\mathbb{T}^d$ with analytic data and prove lower bounds for the radius of spatial analyticity $\epsilon(t)$ of the solution using a new method based on inductive estimates in standard Sobolev spaces. Our…
In this work we study the general system of geodesic equations for the case of a massive particle moving on an arbitrary curved manifold. The investigation is carried out from the symmetry perspective. By exploiting the parametrization…
We consider $L^2$ minimizing geodesics along the group of volume preserving maps $SDiff(D)$ of a given 3-dimensional domain $D$. The corresponding curves describe the motion of an ideal incompressible fluid inside $D$ and are (formally)…
We study the problem of recovering a globally consistent Euclidean embedding of data, given only a local distance graph and propose a method that optimally represents these distances. The method operates solely on a neighborhood graph…
The covariant Poisson equation for Lie algebra-valued mappings defined in 3-dimensional Euclidean space is studied using functional analytic methods. Weighted covariant Sobolev spaces are defined and used to derive sufficient conditions for…
We study the a.s. convergence of a sequence of random embeddings of a fixed manifold into Euclidean spaces of increasing dimensions. We show that the limit is deterministic. As a consequence, we show that many intrinsic functionals of the…
In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite number of deterministic constraints.We investigate the…
We present a novel stabilized isogeometric formulation for the Stokes problem, where the geometry of interest is obtained via overlapping NURBS (non-uniform rational B-spline) patches, i.e., one patch on top of another in an arbitrary but…
We approximate the regular solutions of the incompressible Euler equation by the solution of ODEs on finite-dimensional spaces. Our approach combines Arnold's interpretation of the solution of Euler's equation for incompressible and…
We study the three-dimensional incompressible Euler equations subject to stochastic forcing. We develop a concept of dissipative martingale solutions, where the nonlinear terms are described by generalised Young measures. We construct these…
We propose a finite volume stochastic collocation method for the random Euler system. We rigorously prove the convergence of random finite volume solutions under the assumption that the discrete differential quotients remain bounded in…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
This paper is concerned with the asymptotic behavior of solutions of the two-dimensional Navier-Stokes equations with both non-autonomous deterministic and stochastic terms defined on unbounded domains. We first introduce a continuous…
We integrate in closed implicit form the Navier-Stokes equations for an incompressible fluid and the kinematical dynamo equation, in smooth manifolds and Euclidean space. This integration is carried out by applying Stochastic Differential…
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…