We prove a quantitative regularity theorem and blowup criterion for classical solutions of the
three-dimensional Navier–Stokes equations satisfying certain critical conditions. The …

We prove quantitative regularity and blowup theorems for the incompressible Navier–Stokes
equations in R d \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{…

We establish new non-uniqueness results for the Euler equations with external force on $\mathbb{T}^{d}$
$(d\geq3)$. By introducing a novel alternating convex integration scheme, we …

In storing and transmitting epigenetic information, organisms must balance the need to
maintain information about past conditions with the capacity to respond to information in their …

We establish new non-uniqueness results for the forced inviscid surface quasi-geostrophic
equation, via an alternating formulation of convex integration techniques. Our results imply …

The emergence of self-replication and information transmission in life's origin remains
unexplained despite extensive research on the topic. A hypothesis explaining the transition from a …

We consider the hypodissipative Navier-Stokes equations on $[0,T]\times\mathbb{T}^{d}$
and seek to construct non-unique, H\"older-continuous solutions with epochs of regularity (…

It is assumed that under suitable economic and information-theoretic conditions, market
exchange rates are free from arbitrage. Commodity markets in which trades occur over a …

Consider a velocity field u solving the incompressible Navier-Stokes equations on [0, T]× ℝ
d (d≥ 3) and satisfying∥ u (t)∥ X≤ A for all times, where the norm X is critical with respect …

Members of social networks are given op-portunities to bestow positive recognition upon
one another by means of constructs such as “likes” and “retweets.” Although recipients no …