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In this paper, we are concerned with regularity of nonlocal stochastic partial differential equations of parabolic type. By using Companato estimates and Sobolev embedding theorem, we first show the H\"{o}lder continuity (locally in the…
There is an interplay between models, specified by variables and equations, and their connections to one another. This dichotomy should be reflected in the abstract as well. Without referring to the models directly -- only that a model…
For the Maxwellian molecules or hard potentials case, we verify the smoothing effect for the spatially inhomogeneous Boltzmann equation without angular cutoff. Given initial data with low regularity, we prove its solutions at any positive…
We consider a notion of stability for sheaves, which we call multi-Gieseker stability that depends on several ample polarisations $L_1, \dots, L_N$ and on an additional parameter $\sigma \in \mathbb{Q}_{\geq 0}^N\setminus\{0\}$. The set of…
Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are…
The resolvent formulation of the Navier$\text{--}$Stokes equations gives a means for the characterization and prediction of features of turbulent flows$\text{---}$such as statistics, structures and their nonlinear…
We study the irregularity of hypergeometric D-modules $\mathcal{M}_A (\beta )$ via the explicit construction of Gevrey series solutions along coordinate subspaces in $X =\mathbb{C}^n$. As a consequence, we prove that along coordinate…
In this paper we study the equations governing the unsteady motion of an incompressible homogeneous generalized second grade fluid subject to periodic boundary conditions. We establish the existence of global-in-time strong solutions for…
This article is dedicated to the study of diagonal hyperbolic systems in one space dimension, with cumulative distribution functions, or more generally nonconstant monotonic bounded functions, as initial data. Under a uniform strict…
A regularized Boussinesq equation is studied as a dispersive, long-wave (quasicontinuum) approximation of the Fermi-Pasta-Ulam lattice with a general cubic interaction force. Explicit periodic traveling wave solutions in terms of Jacobi…
We provide a construction of the moduli space of stable coherent sheaves in the world of non-archimedean geometry, where we use the notion of Berkovich non-archimedean analytic spaces. The motivation for our construction is Tony Yue Yu's…
We establish the existence and uniqueness of strong solutions, in both the PDE and probabilistic sense, for a broad class of nonlinear stochastic partial differential equations (SPDEs) on a bounded domain $\mathscr{O}\subset \mathbb{R}^d$…
Often in the analysis of first-order methods for both smooth and nonsmooth optimization, assuming the existence of a growth/error bound or KL condition facilitates much stronger convergence analysis. Hence separate analysis is typically…
We study a mesoscopic model for the flow of amorphous solids. The model is based on the key features identified at the microscopic level, namely peri- ods of elastic deformation interspersed with localised rearrangements of parti- cles that…
This paper investigates the existence, uniqueness, and regularity of solutions to evolution equations with time-measurable pseudo-differential operators in weighted mixed-norm Sobolev-Lipschitz spaces. We also explore trace embedding and…
We study a three-dimensional fluid model describing rapidly rotating convection that takes place in tall columnar structures. The purpose of this model is to investigate the cyclonic and anticyclonic coherent structures. Global existence,…
Using a standard linearization technique and previously obtained microlocal properties for pseudodifferential operators with smooth coefficients, the authors state results of microlocal regularity in generalized Besov spaces for solutions…
Current questions in ecology revolve around instabilities in the dynamics on spatial networks and particularly the effect of node heterogeneity. We extend the Master Stability Function formalism to inhomogeneous biregular networks having…
Stability of inviscid shear shallow water flows with free surface is studied in the framework of the Benney equations. This is done by investigating the generalized hyperbolicity of the integrodifferential Benney system of equations. It is…
We obtain two-bound estimates for the local growth of pluri-subharmonic functions in terms of Siciak and relative extremal functions. As applications, we give simple new proofs of "Bernstein doubling inequality" and the main result in…