Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential
نویسنده
چکیده
The reordering of the multidimensional exponential quadratic operator in coordinatemomentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329–4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.
منابع مشابه
Burgers’ Turbulence Problem with Linear or Quadratic External Potential
We consider solutions of Burgers’ equation with linear or quadratic external potential and stationary random initial conditions of Ornstein–Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.
متن کاملScaling and Exotic Regimes in Decaying Burgers Turbulence
We analyze the stochastic scaling laws arising in the invicid limit of the decaying solutions of the Burgers equation. The linear scaling of the velocity structure functions is shown to reflect the domination by shocks of the long-time asymptotics. We exhibit new self-similar statistics of solutions describing phases with diluted shocks. Some speculations are included on the nature of systems w...
متن کاملMultiscale Analysis for SPDEs with Quadratic Nonlinearities
In this article we derive rigorously amplitude equations for stochastic PDEs with quadratic nonlinearities, under the assumption that the noise acts only on the stable modes and for an appropriate scaling between the distance from bifurcation and the strength of the noise. We show that, due to the presence of two distinct timescales in our system, the noise (which acts only on the fast modes) g...
متن کاملVariational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves
The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...
متن کاملDisordered systems and Burgers’ turbulence
The problem of fully developped turbulence is to characterize the statistical properties of the velocity field of a stirred fluid described by Navier stokes equations. The simplest scaling approach, due to Kolmogorov in 1941, gives a reasonable starting point, but it must be corrected due to the failure of naive scaling giving ‘intermittency’ corrections which are presumably associated with the...
متن کامل