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On a class of stochastic partial differential equations related to turbulent transport
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  • Published: June 1998

On a class of stochastic partial differential equations related to turbulent transport

  • T. Deck1 &
  • J. Potthoff1 

Probability Theory and Related Fields volume 111, pages 101–122 (1998)Cite this article

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  • 14 Citations

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Summary.

We consider the Cauchy problem for the mass density ρ of particles which diffuse in an incompressible fluid. The dynamical behaviour of ρ is modeled by a linear, uniformly parabolic differential equation containing a stochastic vector field. This vector field is interpreted as the velocity field of the fluid in a state of turbulence. Combining a contraction method with techniques from white noise analysis we prove an existence and uniqueness result for the solution ρ∈C 1,2([0,T]×ℝd,(S)*), which is a generalized random field. For a subclass of Cauchy problems we show that ρ actually is a classical random field, i.e. ρ(t,x) is an L 2-random variable for all time and space parameters (t,x)∈[0,T]×ℝd.

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Authors and Affiliations

  1. Fakultät für Mathematik und Informatik, Universität Mannheim, D-68131 Mannheim, Germany e-mail: {deck; potthoff}@math.uni-mannheim.de, , , , , , DE

    T. Deck & J. Potthoff

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  1. T. Deck
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  2. J. Potthoff
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Received: 27 March 1995 / In revised form: 15 May 1997

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Deck, T., Potthoff, J. On a class of stochastic partial differential equations related to turbulent transport. Probab Theory Relat Fields 111, 101–122 (1998). https://doi.org/10.1007/s004400050163

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  • Issue Date: June 1998

  • DOI: https://doi.org/10.1007/s004400050163

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  • Mathematics Subject Classification (1991): 60G20
  • 60H15
  • 60H99
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