Mathematical analysis reveals unique minimal solutions for the multidimensional stochastic Burgers equation, indicating solvable dynamics under Gaussian and Poissonian noise.
We consider the multidimensional Burgers equation with a viscosity erm and a random force modelled by a Gaussian or Poissonian smooth noise, {w(x t)}: We study the connection between this equation and the lowing two tochastic differential equations where , and We prove that the latter equation has a unique non-negative minimalsolution φ(x t), and using the Forsyth-Florin-Hopf-Cole transformation we get solutions h(x t)u(x t) for the two equations above. We study some space-time and Lq estimate for these solutions
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Azzouz Dermoune (1997) studied this question.
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