相关论文: Enhanced dissipation, hypoellipticity for passive …

Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an…

We study models of quintessence consisting of a number of scalar fields coupled to several dark matter components. In the case of exponential potentials the scaling solutions can be described in terms of a single field. The corresponding…

We improve local smoothing estimates for fractional Schr\"{o}dinger equations for $\alpha \in (0,1) \cup (1,\infty)$.

We establish sharp energy decay rates for a large class of nonlinearly first-order damped systems, and we design discretization schemes that inherit of the same energy decay rates, uniformly with respect to the space and/or time…

We consider the statistical inverse problem of estimating a background flow field (e.g., of air or water) from the partial and noisy observation of a passive scalar (e.g., the concentration of a solute), a common experimental approach to…

We consider the advection-diffusion equation \[ \phi_t + Au \cdot \nabla \phi = \Delta \phi, \qquad \phi(0,x)=\phi_0(x) \] on $\bbR^2$, with $u$ a periodic incompressible flow and $A\gg 1$ its amplitude. We provide a sharp characterization…

We consider evolution of a passive scalar (concentration of pollutants or temperature) in a chaotic (turbulent) flow. A universal asymptotic behavior of the passive scalar decay (homogenization) related to peripheral regions (near walls) is…

We consider active suspensions in the isotropic phase subjected to a shear flow. Using a set of extended hydrodynamic equations we derive a variety of {\em analytical} expressions for rheological quantities such as shear viscosity and…

We show how to adapt the approach introduced for viscous damping in [1] to derive the approximate amplitude decay in the case of damping by a force of constant magnitude (sliding friction) and in the case of damping by a force proportional…

We consider the problem of existence of entropy weak solutions to scalar balance laws with a dissipative source term. The flux function may be discontinuous with respect both to the space variable x and the unknown quantity u. The problem…

We establish a rate of convergence of the two scale expansion (in the sense of homogenization theory) of the solution to a highly oscillatory elliptic partial differential equation with random coefficients that are a perturbation of…

Probability density function (PDF) of passive scalar dissipation ${\cal P} (\epsilon)$ is found analytically in the limit of large Peclet and Prandtl numbers (Batchelor-Kraichnan regime) in two dimensions. The tail of PDF at…

We introduce novel entropy-dissipative numerical schemes for a class of kinetic equations, leveraging the recently introduced scalar auxiliary variable (SAV) approach. Both first and second order schemes are constructed. Since the…

We introduce a new framework to deal with rough differential equations based on flows and their approximations. Our main result is to prove that measurable flows exist under weak conditions, even solutions to the corresponding rough…

Mixed-dimensional elliptic equations exhibiting a hierarchical structure are commonly used to model problems with high aspect ratio inclusions, such as flow in fractured porous media. We derive general abstract estimates based on the theory…

We report the results of simulations of rigid colloidal helices suspended in a shear flow, using dissipative particle dynamics for a coarse-grained representation of the suspending fluid, as well as deterministic trajectories of…

Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…

We prove, for a wide class of semilinear elliptic differential and pseudodifferential equations in $\R^d$, that the solutions which are sufficiently regular and have a certain decay at infinity extend to holomorphic functions in sectors of…

We construct a class of infinite mass functions for which solutions of the viscous Burgers equation decay at a better rate than solution of the heat equation for initial data in this class. In other words, we show an enhanced dissipation…