22 citations · 71 across the 15 of their papers we have counts for
16 papers
Navier-Stokes Equations with Fractional Dissipation and Associated Doubly Stochastic Yule Cascades
Radu Dascaliuc, Tuan N. Pham, Enrique Thomann +1
We introduce a self-similar doubly stochastic Yule (DSY) cascade associated with the deterministic Navier-Stokes equations (NSE) in with fractional dissipation $(-Δ)…
Transformation of Stochastic Recursions and Critical Phenomena in the Analysis of the Aldous-Shields-Athreya Cascade and Related Mean Flow Equations
Radu Dascaliuc, Tuan N. Pham, Enrique Thomann +1
The paper has two main goals. First, we extend the contemporary probability theory on trees to investigate critical phenomena in a stochastic model of Yule type called Aldous-Shiel…
Errata to Stochastic explosion and non-uniqueness for -Riccati equation
Radu Dascaliuc, Tuan N. Pham, Enrique A. Thomann +1
An error occurs in a part of the statement and proof of Proposition 2.2 in Jour. Math. Anal. and Appl., 476, (2019), 53-85 that is corrected in this erratum. The revised result rev…
Doubly stochastic Yule cascades (Part II): The explosion problem in the non-reversible case
Radu Dascaliuc, Tuan N. Pham, Enrique Thomann +1
We analyze the explosion problem for a class of stochastic models introduced in Part I (arXiv:2103.06912), referred to as doubly stochastic Yule cascades. These models arise natura…
On Le Jan-Sznitman's stochastic approach to the Navier-Stokes equations
Radu Dascaliuc, Tuan N. Pham, Enrique Thomann
The paper explores the symbiotic relation between the Navier-Stokes equations and the associated stochastic cascades. Specifically, we examine how some well-known existence and uni…
A Delayed Yule Process
Radu Dascaliuc, Nicholas Michalowski, Enrique Thomann +1
In now classic work, David Kendall (1966) recognized that the Yule process and Poisson process could be related by a (random) time change. Furthermore, he showed that the Yule popu…
Symmetry Breaking and Uniqueness for the Incompressible Navier-Stokes Equations
Radu Dascaliuc, Nicholas Michalowski, Enrique Thomann +1
The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar…
Effect of vorticity coherence on energy-enstrophy bounds for the 3D Navier-Stokes equations
Radu Dascaliuc, Zoran Grujić, Michael S. Jolly
Bounding curves in the energy,enstrophy-plane are derived for the 3D Navier-Stokes equations under an assumption on coherence of the vorticity direction. The analysis in the critic…
On energy cascades in non-homogeneous 3D Navier-Stokes equations
R. Dascaliuc, Z. Grujić
We show - in the framework of physical scales and -averages - that Kolmogorov's dissipation law combined with the smallness condition on a Taylor length scale are suffic…
Vortex stretching and criticality for the 3D NSE
R. Dascaliuc, Z. Grujić
A mathematical evidence -- in a statistically significant sense -- of a geometric scenario leading to criticality of the Navier-Stokes problem is presented.
Coherent vortex structures and 3D enstrophy cascade
R. Dascaliuc, Z. Grujić
Existence of 2D enstrophy cascade in a suitable mathematical setting, and under suitable conditions compatible with 2D turbulence phenomenology, is known both in the Fourier and in…
Energy cascades and flux locality in physical scales of the 3D Navier-Stokes equations
R. Dascaliuc, Z. Grujic
Rigorous estimates for the total - (kinetic) energy plus pressure - flux in R^3 are obtained from the three dimensional Navier-Stokes equations. The bounds are used to establish a…
Dissipation anomaly and energy cascade in 3D incompressible flows
Radu Dascaliuc, Zoran Grujić
The purpose of this note is to present a mathematical evidence of dissipation anomaly in 3D turbulent flows within a general setting for the study of energy cascade in physical sca…
Anomalous dissipation and energy cascade in 3D inviscid flows
Radu Dascaliuc, Zoran Grujić
Adopting the setting for the study of existence and scale locality of the energy cascade in 3D viscous flows in physical space recently introduced by the authors to 3D inviscid flo…
2D turbulence in physical scales of the Navier-Stokes equations
R. Dascaliuc, Z. Grujic
Local analysis of the two dimensional Navier-Stokes equations is used to obtain estimates on the energy and enstrophy fluxes involving Taylor and Kraichnan length scales and the si…
A strengthening of the energy inequality for the Leray-Hopf solutions of the 3D periodic Navier-Stokes equations
Radu Dascaliuc
In present note we establish the following inequality for the the Leray-Hopf solutions of the 3-D -periodic Navier-Stokes Equations: \[ϕ(|u(t)|^2)-ϕ(|u(t_0)|^2)\le 2\int_{t_0}^{…