10 papers · 1 filter
On the absence of blow-up in the 3D Navier-Stokes equations with transport noise
Antonio Agresti
Establishing the global-in-time smoothness of solutions to the 3D Navier-Stokes equations (NSEs) with large initial data remains a long-standing open problem. In this paper, we pro…
Global smooth solutions by high mode Lie-Transport noise for Logarithmically Hyperdissipative Navier-Stokes equations
Antonio Agresti, Federico Butori, Eliseo Luongo
We study a logarithmically hyperviscous Navier-Stokes model on the three-dimensional torus with Lie-transport noise, which includes both transport and stretching. We prove that, fo…
Fractal dimension of singular times for SPDEs: Energy bounds, criticality, and weak-strong uniqueness
Antonio Agresti
For several physically relevant SPDEs, it is known that global weak solutions coexist with local strong ones. Typically, weak-strong uniqueness results are known, and ensure that t…
Sharp bounds for non-trace class noise and applications to SPDEs
Antonio Agresti, Fabian Germ, Mark Veraar
In the study of stochastic PDEs with colored, non-trace class space-time noise, one frequently encounters Gaussian series of the form where $(γ_n…
The large deviation principle for the stochastic 3D primitive equations with transport noise
Antonio Agresti, Esmée Theewis
We prove the small-noise large deviation principle for the three-dimensional primitive equations with transport noise and turbulent pressure. Transport noise is important for geoph…
A stochastic flow approach to De Giorgi-Nash-Moser estimates for SPDEs with smooth transport noise
Antonio Agresti, Max Sauerbrey, Mark Veraar
The celebrated De Giorgi-Nash-Moser theory ensures that solutions to uniformly elliptic or parabolic PDEs are bounded and Hölder continuous, even with merely bounded measurable coe…
A Note on a threshold for temporal regularity of stochastic PDEs
Antonio Agresti, Mark Veraar
We consider solutions to linear parabolic SPDEs of the form \[ \mathrm{d} u(t) + A u(t)\, \mathrm{d} t = g(t)\, \mathrm{d} β, \qquad u(0)=0, \] where is a positive, invertible,…
Lagrangian chaos and unique ergodicity for stochastic primitive equations
Antonio Agresti
We show that the Lagrangian flow associated with the stochastic 3D primitive equations (PEs) with non-degenerate noise is chaotic, i.e., the corresponding top Lyapunov exponent is…
Nonlinear SPDEs and Maximal Regularity: An Extended Survey
Antonio Agresti, Mark Veraar
In this survey, we provide an in-depth exposition of our recent results on the well-posedness theory for stochastic evolution equations, employing maximal regularity techniques. Th…
The critical variational setting for stochastic evolution equations
Antonio Agresti, Mark Veraar
In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi- or semi-linear type. Our results improve many of the abstract res…