Critical phenomena in gravitational collapse

C Gundlach, JM Martin-Garcia - Living Reviews in Relativity, 2007‏ - Springer
As first discovered by Choptuik, the black hole threshold in the space of initial data for
general relativity shows both surprising structure and surprising simplicity. Universality …

The influence of boundaries on gravity currents and thin films: drainage, confinement, convergence, and deformation effects

Z Zheng, HA Stone - Annual Review of Fluid Mechanics, 2022‏ - annualreviews.org
Thin film flows, whether driven by gravity, surface tension, or the relaxation of elastic
boundaries, occur in many natural and industrial processes. Applications span problems of …

Beyond kolmogorov cascades

B Dubrulle - Journal of Fluid Mechanics, 2019‏ - cambridge.org
The large-scale structure of many turbulent flows encountered in practical situations such as
aeronautics, industry, meteorology is nowadays successfully computed using the …

[کتاب][B] Random Perturbation of PDEs and Fluid Dynamic Models: École d'été de Probabilités de Saint-Flour XL–2010

F Flandoli - 2011‏ - books.google.com
This volume deals with the random perturbation of PDEs which lack well-posedness, mainly
because of their non-uniqueness, in some cases because of blow-up. The aim is to show …

[کتاب][B] Nonlinear partial differential equations: Asymptotic behavior of solutions and self-similar solutions

MH Giga, Y Giga, J Saal - 2010‏ - books.google.com
The purpose of this book is to present typical methods (including rescaling methods) for the
examination of the behavior of solutions of nonlinear partial di? erential equations of di …

Formation of shocks for 2D isentropic compressible Euler

T Buckmaster, S Shkoller, V Vicol - Communications on Pure …, 2022‏ - Wiley Online Library
We consider the 2D isentropic compressible Euler equations, with pressure law p (ρ)=(1 γ) ρ
γ, with γ> 1. We provide an elementary constructive proof of shock formation from smooth …

Formation of point shocks for 3D compressible Euler

T Buckmaster, S Shkoller, V Vicol - Communications on Pure …, 2023‏ - Wiley Online Library
We consider the 3D isentropic compressible Euler equations with the ideal gas law. We
provide a constructive proof of the formation of the first point shock from smooth initial datum …

Pointy ice-drops: How water freezes into a singular shape

JH Snoeijer, P Brunet - American Journal of Physics, 2012‏ - pubs.aip.org
A water drop that is gently deposited on a very cold surface freezes into a pointy ice-drop
with a very sharp tip. The formation of this singular shape originates from the reduction of …

Asymptotic self-similar blow-up profile for three-dimensional axisymmetric Euler equations using neural networks

Y Wang, CY Lai, J Gómez-Serrano, T Buckmaster - Physical Review Letters, 2023‏ - APS
Whether there exist finite-time blow-up solutions for the 2D Boussinesq and the 3D Euler
equations are of fundamental importance to the field of fluid mechanics. We develop a new …

Swelling instability of surface-attached gels as a model of soft tissue growth under geometric constraints

MB Amar, P Ciarletta - Journal of the Mechanics and Physics of Solids, 2010‏ - Elsevier
The purpose of this work is to provide a theoretical analysis of the mechanical behavior of
the growth of soft materials under geometrical constraints. In particular, we focus on the …