On a class of stochastic partial differential equations related to turbulent transport |
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Authors: | T Deck J Potthoff |
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Institution: | Fakult?t für Mathematik und Informatik, Universit?t Mannheim, D-68131 Mannheim, Germany e-mail: {deck; potthoff}@math.uni-mannheim.de, DE
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Abstract: | 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]×ℝ
d
,(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]×ℝ
d
.
Received: 27 March 1995 / In revised form: 15 May 1997 |
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Keywords: | Mathematics Subject Classification (1991): 60G20 60H15 60H99 |
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