2D Navier–Stokes equation with cylindrical fractional Brownian noise
نویسندگان
چکیده
منابع مشابه
The Fractional Langevin Equation: Brownian Motion Revisited
It is well known that the concept of diffusion is associated with random motion of particles in space, usually denoted as Brownian motion, see e.g. [1-3]. Diffusion is considered normal when the mean squared displacement of the particle during a time interval becomes, for sufficiently long intervals, a linear function of it. When this linearity breaks down, degenerating in a power law with expo...
متن کاملTwo-dimensional Stochastic Navier-stokes Equations with Fractional Brownian Noise
We study the perturbation of the two-dimensional stochastic Navier-Stokes equation by a Hilbert-space-valued fractional Brownian noise. Each Hilbert component is a scalar fractional Brownian noise in time, with a common Hurst parameter H and a specific intensity. Because the noise is additive, simple Wiener-type integrals are suffi cient for properly defining the problem. It is resolved by sepa...
متن کاملSolutions to Time-Fractional Diffusion-Wave Equation in Cylindrical Coordinates
Nonaxisymmetric solutions to time-fractional diffusion-wave equation with a source term in cylindrical coordinates are obtained for an infinite medium. The solutions are found using the Laplace transform with respect to time t, the Hankel transform with respect to the radial coordinate r, the finite Fourier transform with respect to the angular coordinate φ, and the exponential Fourier transfor...
متن کاملFractional Diffusion Equation in Cylindrical Symmetry: A New Derivation
Diffusion is one of the basic nonequilibrium processes that is of great interest in physicas and many other field. Normal diffusion and its simulation obey Gaussian statistics and can be characterized by meansquare displacement that is asymptotic linear in time, i. e., < r(t)2 >∼ t, where r is the distance the walker has travelled in the time t from the starting point. In many physical systems ...
متن کاملStochastic Heat Equation with Multiplicative Fractional-Colored Noise
We consider the stochastic heat equation with multiplicative noise ut = 1 2 ∆u + uẆ in R+ × R , whose solution is interpreted in the mild sense. The noise Ẇ is fractional in time (with Hurst index H ≥ 1/2), and colored in space (with spatial covariance kernel f). When H > 1/2, the equation generalizes the Itô-sense equation for H = 1/2. We prove that if f is the Riesz kernel of order α, or the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annali di Matematica Pura ed Applicata (1923 -)
سال: 2018
ISSN: 0373-3114,1618-1891
DOI: 10.1007/s10231-018-0809-x