Abstract
In this chapter a solution of the Navier-Stokes system in a bounded domain is constructed for the case when external forces include random fluctuations of white noise type. In this case a solution u (t, x) of the Navier-Stokes system is also a random function. The energy integral contains the trace of the white noise correlation operator which follows from the Ito formula for differentiation of the energy of a random flow.
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© 1988 Kluwer Academic Publishers
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Vishik, M.J., Fursikov, A.V. (1988). Navier-Stokes System with White Noise in a Bounded Domain. In: Mathematical Problems of Statistical Hydromechanics. Mathematics and Its Applications (Soviet Series), vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1423-0_11
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DOI: https://doi.org/10.1007/978-94-009-1423-0_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7137-6
Online ISBN: 978-94-009-1423-0
eBook Packages: Springer Book Archive