Related papers: Flows driven by Banach space-valued rough paths
Shallow flow or thin liquid film models are used for a wide range of physical and engineering problems. Shallow flow models allow capturing the free surface of the fluid with little effort and reducing the three-dimensional problem to a…
The Cauchy problem for a multidimensional linear transport equation with unbounded drift is investigated. Provided the drift is Holder continuous , existence, uniqueness and strong stability of solutions are obtained. The proofs are based…
Versions of the Oseledets multiplicative ergodic theorem for cocycles acting on infinite-dimensional Banach spaces have been investigated since the pioneering work of Ruelle in 1982 and are a topic of continuing research interest. For a…
In this work, we analytically derive the exact closed dynamical equations for a liquid with short-ranged interactions in large spatial dimensions using the same statistical mechanics tools employed to analyze Brownian motion. Our derivation…
We introduce the class of "smooth rough paths" and study their main properties. Working in a smooth setting allows us to discard sewing arguments and focus on algebraic and geometric aspects. Specifically, a Maurer-Cartan perspective is the…
We propose and analyze a mixed formulation for the Brinkman-Forchheimer equations for unsteady flows. Our approach is based on the introduction of a pseudostress tensor related to the velocity gradient, leading to a mixed formulation where…
Linking numbers in higher dimensions and their generalization including gauge fields are studied in the context of BF theories. The linking numbers associated to $n$-manifolds with smooth flows generated by divergence-free p-vector fields,…
We develop a set of techniques that enable us to effectively recover Besov rough analysis from p-variation rough analysis. Central to our approach are new metric groups, in which some objects in rough path theory that have been previously…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
Having been unclear how to define that a domain is strictly pseudoconvex in the infinite-dimensional setting, we develop a general theory having Banach spaces in mind. We first focus on finite dimension and eliminate the need of two degrees…
In this paper we study the convergence of a power-law model for dilatant compressible fluids to a class of models exhibiting a maximum admissible shear rate, called thick compressible fluids. These kinds of problems were studied previously…
Cauchy invariants are now viewed as a powerful tool for investigating the Lagrangian structure of three-dimensional (3D) ideal flow (Frisch & Zheligovsky, Commun. Math. Phys., vol. 326, 2014, pp. 499-505, Podvigina et al., J. Comput. Phys.,…
We analyze the problem for viscous incompressible heat-conduc\-ting fluid in a finite cylinder with large inflow and outflow, modelled with Navier-Stokes equations coupled with the heat equation. We prove energy estimate without…
In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We…
We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…
We prove that a locally bounded and differentiable in the sense of Gateaux function given in a finite-dimensional commutative Banach algebra over the complex field is also differentiable in the sense of Lorch.
A detailed analysis is presented to demonstrate the capabilities of the lattice Boltzmann method. Thorough comparisons with other numerical solutions for the two-dimensional, driven cavity flow show that the lattice Boltzmann method gives…
The Jones-Witten invariants can be generalized for non-singular smooth vector fields with invariant probability measure on 3-manifolds, giving rise to new invariants of dynamical systems [22]. After a short survey of cohomological field…
Prandtl's secondary flows of the second kind generated by laterally-varying roughness are studied using the linearised Reynolds-Averaged Navier-Stokes approach proposed in Zampino et al (2022). The momentum equations are coupled to the…