In this paper we review many aspects of the well-posedness theory for the Cauchy problem
for the continuity and transport equations and for the ordinary differential equation (ODE). In …

Abstract The Obukhov–Corrsin theory of scalar turbulence [,] advances quantitative
predictions on passive-scalar advection in a turbulent regime and can be regarded as the …

We study the problem of the optimal mixing of a passive scalar under the action of an
incompressible flow in two space dimensions. The scalar solves the continuity equation with …

Counterfactual inference aims to answer retrospective" what if" questions and thus belongs
to the most fine-grained type of inference in Pearl's causality ladder. Existing methods for …

We study anomalous dissipation in hydrodynamic turbulence in the context of passive
scalars. Our main result produces an incompressible C^ ∞ (0, T) * T^ d) ∩ L^ 1 (0, T; C^ 1 …

In this paper, we prove an extended version of the Minkowski Inequality, holding for any
smooth bounded set Ω⊂ R n, n≥ 3. Our proof relies on the discovery of effective …

Given a vector field ρ (1, b) ∈ L^ 1_ loc (R^+ * R^ d, R^ d+ 1) ρ (1, b)∈ L loc 1 (R+× R d, R
d+ 1) such that\, div\, _ t, x (ρ (1, b)) div t, x (ρ (1, b)) is a measure, we consider the problem of …

We characterize the autonomous, divergence-free vector fields b on the plane such that the
Cauchy problem for the continuity equation∂ tu+ div (bu)= 0 admits a unique bounded …

We consider Bayesian optimization using Gaussian Process models, also referred to as
kernel-based bandit optimization. We study the methodology of exploring the domain using …

We study first-and second-order linear transport equations, as well as flows for ordinary and
stochastic differential equations, with irregular velocity fields satisfying a one-sided Lipschitz …