Stochastic heat and Burgers equations and their singularities. I. Geometrical properties

DOI10.1063/1.1471925zbMath1060.60063OpenAlexW2092956905MaRDI QIDQ4832662

Ian M. Davies, Huaizhong Zhao, Aubrey Truman

Publication date: 14 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://figshare.com/articles/Stochastic_heat_and_Burgers_equations_and_their_singularities_I_Geometrical_properties/9383444

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Stochastic analysis applied to problems in fluid mechanics (76M35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items

Representation of solutions of the Burgers equation using functional integrals ⋮ Geometric properties of the Maxwell set and a vortex filament structure for Burgers equation ⋮ Fractional stochastic active scalar equations generalizing the multi-dimensional quasi-geostrophic \& 2D-Navier-Stokes equations: the general case ⋮ Stochastic Burgers PDEs with random coefficients and a generalization of the Cole-Hopf transformation ⋮ BURGERS EQUATION AND KOLMOGOROV–PETROVSKY–PISKUNOV EQUATION ON MANIFOLDS ⋮ Stochastic heat and Burgers equations and their singularities. II. Analytical properties and limiting distributions ⋮ О точности разностной схемы для уравнений Навье - Стокса ⋮ The stochastic Burgers equation with vorticity: Semiclassical asymptotic series solutions with applications

Cites Work

• Asymptotic analysis of Gaussian integrals. II: Manifold of minimum points
• Laplace's method for Gaussian integrals with an application to statistical mechanics
• Stochastic Burgers' equations and their semi-classical expansions
• The stochastic Burgers equation
• Stratified structure of the Universe and Burgers' equation -- a probabilistic approach
• The Burgers equation with a random force and a general model for directed polymers in random environments
• On the large time asymptotics of decaying Burgers turbulence
• Invariant measures for Burgers equation with stochastic forcing
• On the stochastic Burgers' equation in the real line
• Laplace asymptotic expansions of conditional Wiener integrals and generalised Mehler kernel formulae for Hamiltonians on L²(Rⁿ)
• Dynamic Scaling of Growing Interfaces
• On the Laplace asymptotic expansion of conditional Wiener integrals and the Bender–Wu formula for x2N-anharmonic oscillators
• Stochastic Navier-stokes equations with multiplicative noise
• The burgers equation with a noisy force and the stochastic heat equation
• Probabilistic approach to the small viscosity asymptotics for Navier-Stokes equations
• Statistical theory for the stochastic Burgers equation in the inviscid limit
• Quantum mechanics of charged particles in random electromagnetic fields
• Stochastic Burgers' equation

This page was built for publication: Stochastic heat and Burgers equations and their singularities. I. Geometrical properties