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Motivated by numerical schemes for large scale geophysical flow, we consider the rotating shallow water and Boussinesq equations on the whole space with horizontal kinetic energy backscatter source terms built from negative viscosity and…
Fluid deformation controls myriad processes in random flows including mixing and dispersion, stress development in complex fluids, colloid transport and deposition, droplet breakup and emulsification, fluid-structure interaction, chemical…
It is well-known (see Dvoretzky, Erd{\H o}s and Kakutani [8] and Le Gall [12]) that a planar Brownian motion $(B_t)_{t\ge 0}$ has points of infinite multiplicity, and these points form a dense set on the range. Our main result is the…
This paper studies, in dimensions greater than two, stationary diffusion processes in random environment which are small, isotropic perturbations of Brownian motion satisfying a finite range dependence. Such processes were first considered…
This theoretical study deals with the Navier-Stokes equations posed in a 3D thin domain with thickness $0<\varepsilon\ll 1$, assuming power law slip boundary conditions, with an anisotropic tensor, on the bottom. This condition, introduced…
This paper provides information about the asymptotic behavior of a one-dimensional Brownian polymer in random medium represented by a space-time Gaussian field W assumed to be white noise in time and function-valued in space. According to…
We investigate the stability and global existence of weak solutions to a free boundary problem governing the evolution of polymeric fluids. We construct weak solutions of the two-phase model by performing the asymptotic limit of a…
We study the long time existence theory for a non local flow associated to a free boundary problem for a trapped non liquid drop. The drop has free boundary components on two horizontal plates and its free energy is anisotropic and axially…
We provide a rigorous derivation of the brownian motion as the limit of a deterministic system of hard-spheres as the number of particles $N$ goes to infinity and their diameter $\varepsilon$ simultaneously goes to $0$, in the fast…
Initial-boundary value problem for linearized equations of motion of viscous barotropic fluid in a bounded domain is considered. Existence, uniqueness and estimates of weak solutions to this problem are derived. Convergence of the solutions…
We consider one-dimensional Brownian motion conditioned (in a suitable sense) to have a local time at every point and at every moment bounded by some fixed constant. Our main result shows that a phenomenon of entropic repulsion occurs: that…
We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function…
It is well-known that stable and unstable manifolds strongly influence fluid motion in unsteady flows. These emanate from hyperbolic trajectories, with the structures moving nonautonomously in time. The local directions of emanation at each…
The slow viscous flow through a doubly-periodic array of cylinders does not have an analytical solution. However, as a reduced model for the flow within fibrous porous media, this solution is important for many real-world systems. We…
We consider the system of equations describing the flow of incompressible fluids in bounded domain. In the considered setting, the Cauchy stress tensor is a monotone mapping and has asymptotically $(s-1)$-growth with the parameter $s$…
Central limit theorems and asymptotic properties of the minimum-contrast estimators of the drift parameter in linear stochastic evolution equations driven by fractional Brownian motion are studied. Both singular ($H < \frac{1}{2})$ and…
Spherically symmetric expansionfree distributions are systematically studied. The whole set of field equations and junction conditions are presented for a general distribution of dissipative anisotropic fluid (principal stresses unequal),…
The three-dimensional shapes of thin lamina such as leaves, flowers, feathers, wings etc, are driven by the differential strain induced by the relative growth. The growth takes place through variations in the Riemannian metric, given on the…
Pursuing the approach of Angel & Ray, we introduce and study a family of random infinite triangulations of the full-plane that satisfy a natural spatial Markov property. These new random lattices naturally generalize Angel & Schramm's…
The late time evolution of Friedmann-Robertson-Walker (FRW) models with a perfect fluid matter source is studied in the conformal frame of $f(R) $ gravity. We assume that the corresponding scalar field, nonminimally coupled to matter, has…