Related papers: On a class of forced active scalar equations with …
We present a data-driven framework for learning hydrodynamic equations from particle-based simulations of active matter. Our method leverages coarse-graining in both space and time to bridge microscopic particle dynamics with macroscopic…
Additive noise in Partial Differential equations, in particular those of fluid mechanics, has relatively natural motivations. The aim of this work is showing that suitable multiscale arguments lead rigorously, from a model of fluid with…
We show that a general class of active scalar equations, including porous media and certain magnetostrophic turbulence models, admit non-unique weak solutions in the class of bounded functions. The proof is based upon the method of convex…
Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…
Diffusion is the macroscopic manifestation of disordered molecular motion. Mathematically, diffusion equations are partial differential equations describing the fluid-like large-scale dynamics of parcels of molecules. Spatially…
We establish the long-time existence of large-data weak solutions to a system of nonlinear partial differential equations. The system of interest governs the motion of non-Newtonian fluids described by a simplified viscoelastic rate-type…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…
Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…
Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. For example, when solving equations related to fluid dynamics for systems with a large Reynolds number, sub-grid effects…
In this paper, we study the dynamics of a finite number of spherical bubbles in a compressible fluid within a bounded open domain of R 3 . The fluid-bubble interaction is described by a system of nonlinear partial differential equations…
The one-dimensional fractional derivative Maxwell model (e.g. Palade et al. Rheol. Acta 35, 265, 1996), of importance in modeling the linear viscoelastic response in the glass transition region, has been generalized in Palade et al. Int. J.…
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…
The modeling of multi-phase flow is very challenging, given the range of scales as well as the diversity of flow regimes that one encounters in this context. We revisit the discrete equation method (DEM) for two-phase flow in the absence of…
We consider the system of partial differential equations governing two-dimensional flows of a robust class of viscoelastic rate-type fluids with stress diffusion, involving a general objective derivative. The studied system generalizes the…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…
A framework to establish response theory for a class of nonlinear stochastic partial differential equations (SPDEs) is provided. More specifically, it is shown that for a certain class of observables, the averages of those observables…
Many physical systems are governed by ordinary or partial differential equations (see, for example, Chapter ''Differential equations'', ''System of Differential Equations''). Typically the solution of such systems are functions of time or…
In this article we initiate the mathematical study of the dynamics of a system of nonlinear Partial Differential Equations modelling the motion of incompressible, isothermal and conducting modified bipolar fluids in presence of magnetic…