相关论文: Anomalous Regularization in Kazantsev-Kraichnan Mo…
We prove strong well-posedness results for the stochastic 2D Euler equations in vorticity form and generalized SQG equations, with $L^p$ initial data and driven by a spatially rough, incompressible transport noise of Kraichnan type.…
The problem of the effects of compressibility and large-scale anisotropy on anomalous scaling behavior is considered for two models describing passive advection of scalar density and tracer fields. The advecting velocity field is Gaussian,…
For scalar field theory, a new generalization of the Exact RG to curved space is proposed, in which the conformal anomaly is explicitly present. Vacuum terms require regularization beyond that present in the canonical formulation of the…
This work addresses the question of uniqueness and regularity of the minimizers of a convex but not strictly convex integral functional with linear growth in a two-dimensional setting. The integrand -- whose precise form derives directly…
We investigate the behavior of fluid trajectories in a multifractal extension of the Kraichnan model of turbulent advection. The model couples a one-dimensional, Gaussian, white-in-time random flow to a frozen-in-time Gaussian…
We study anomalous dissipation in the context of passive scalars and we construct a two-dimensional autonomous divergence-free velocity field in $C^\alpha$ (with $\alpha \in (0,1)$ arbitrary but fixed) which exhibits anomalous dissipation.…
We present the first study of the dynamic scaling or multiscaling of passive-scalar and passive-vector turbulence. For the Kraichnan version of passive-scalar and passive-vector turbulence we show analytically, in both Eulerian and…
In this work we rigorously establish a number of properties of "turbulent" solutions to the stochastic transport and the stochastic continuity equations constructed by Le Jan and Raimond in [Ann. Probab. 30(2): 826-873, 2002]. The advecting…
The problem of the interplay between normal and anomalous scaling in turbulent systems stirred by a random forcing with a power law spectrum is addressed. We consider both linear and nonlinear systems. As for the linear case, we study…
We study the stochastic Kardar-Parisi-Zhang equation for kinetic roughening where the time-independent (columnar or spatially quenched) Gaussian random noise $f(t,{\bf x})$ is specified by the pair correlation function $\langle f(t,{\bf…
Based on the mechanics of the Euler equation at short time, we show that a Recent Fluid Deformation (RFD) closure for the vorticity field, neglecting the early stage of advection of fluid particles, allows to build a 3D incompressible…
We study effects of turbulent mixing on the random growth of an interface in the problem of the deposition of a substance on a substrate. The growth is modelled by the well-known Kardar--Parisi--Zhang model. The turbulent advecting velocity…
The asymptotic decay of passive scalar fields is solved analytically for the Kraichnan model, where the velocity has a short correlation time. At long times, two universality classes are found, both characterized by a distribution of the…
We consider the persistence phenomenon in advectecd passive scalar equation in 1-dimension. The velocity field is random with the $<v(k,\omega)v(-k,-\omega) > \sim |k|^{-(2+\alpha)}$. In presence of the non-linearity the complete Green's…
We investigate under which assumptions the flow associated to autonomous planar vector fields inherits the Sobolev or BV regularity of the vector field. We consider nearly incompressible and divergence-free vector fields, taking advantage…
Forced advection of passive tracer, $\theta $, in nonlinear relaxational medium by large scale (Batchelor problem) incompressible velocity field at scales less than the correlation length of the flow and larger than the diffusion scale is…
For any $\beta_0<1/3$ we construct divergence free vector fields in $ C_{x,t}^{\beta_0}$ and a sequence of diffusivities $\kappa_q \searrow 0$ such that, for an arbitrary initial datum from a low regularity class, the classical solution…
The trace anomaly and anomaly-induced action are evaluated for the two-dimensional $2D$ vector theory with classical conformal symmetry. Implementing local conformal symmetry while preserving the gauge invariance requires either giving up…
Fluid turbulence is a far-from-equilibrium phenomenon and remains one of the most challenging problems in physics. Two-dimensional, fully developed turbulence may possess the largest possible symmetry, the conformal symmetry. We focus on…
The renormalization group and operator product expansion are applied to the model of a passive scalar quantity advected by the Gaussian self-similar velocity field with finite, and not small, correlation time. The inertial-range energy…