[ספר][B] Encyclopedia of nonlinear science

A Scott - 2006‏ - taylorfrancis.com
In 438 alphabetically-arranged essays, this work provides a useful overview of the core
mathematical background for nonlinear science, as well as its applications to key problems …

Harmonic analysis tools for solving the incompressible Navier–Stokes equations

M Cannone - Handbook of mathematical fluid dynamics, 2005‏ - Elsevier
Formulated and intensively studied at the beginning of the nineteenth century, the classical
partial differential equations of mathematical physics represent the foundation of our …

[ספר][B] Random walk, Brownian motion, and martingales

RN Bhattacharya, EC Waymire - 2021‏ - Springer
The theory of stochastic processes has numerous and longstanding significant interactions
with pure and applied mathematics as well as most branches of physical and biological …

A stochastic Lagrangian representation of the three‐dimensional incompressible Navier‐Stokes equations

P Constantin, G Iyer - … on Pure and Applied Mathematics: A …, 2008‏ - Wiley Online Library
In this paper we derive a probabilistic representation of the deterministic three‐dimensional
Navier‐Stokes equations based on stochastic Lagrangian paths. The particle trajectories …

Probability & incompressible Navier-Stokes equations: An overview of some recent developments

EC Waymire - 2005‏ - projecteuclid.org
This is largely an attempt to provide probabilists some orientation to an important class of
non-linear partial differential equations in applied mathematics, the incompressible Navier …

A stochastic-Lagrangian approach to the Navier–Stokes equations in domains with boundary

P Constantin, G Iyer - 2011‏ - projecteuclid.org
In this paper we derive a probabilistic representation of the deterministic 3-dimensional
Navier–Stokes equations in the presence of spatial boundaries. The formulation in the …

Harmonic analysis of Mandelbrot cascades--in the context of vector-valued martingales

X Chen, Y Han, Y Qiu, Z Wang - arxiv preprint arxiv:2409.13164, 2024‏ - arxiv.org
We solve a long-standing open problem of determining the Fourier dimension of the
Mandelbrot canonical cascade measure (MCCM). This problem of significant interest was …

The fundamental solution of the linearized Navier–Stokes equations for spinning bodies in three spatial dimensions–time dependent case

EA Thomann, RB Guenther - Journal of Mathematical Fluid Mechanics, 2006‏ - Springer
Explicit formulae for the fundamental solution of the linearized time dependent Navier–
Stokes equations in three spatial dimensions are obtained. The linear equations considered …

[HTML][HTML] Stochastic solutions and singular partial differential equations

RV Mendes - Communications in Nonlinear Science and Numerical …, 2023‏ - Elsevier
Stochastic solutions is a robust technique previously used to obtain new exact solutions for
deterministic nonlinear partial differential equations as well as numerical algorithms suited …

Doubly stochastic Yule cascades (Part I): The explosion problem in the time-reversible case

R Dascaliuc, TN Pham, E Thomann… - Journal of Functional …, 2023‏ - Elsevier
Motivated by the probabilistic methods for nonlinear differential equations introduced by
McKean (1975) for the Kolmogorov-Petrovski-Piskunov (KPP) equation, and by Le Jan and …