Noise prevents singularities in linear transport equations

作者：Fedrizzi E^*; Flandoli F

来源：Journal of Functional Analysis, 2013, 264(6): 1329-1354.

DOI：10.1016/j.jfa.2013.01.003

• Stochastic linear transport equation
• No-blow-up
• Integrable drift
• Sobolev initial conditions

A stochastic linear transport equation with multiplicative noise is considered and the question of no-blow-up is investigated. The drift is assumed only integrable to a certain power. Opposite to the deterministic case where smooth initial conditions may develop discontinuities, we prove that a certain Sobolev degree of regularity is maintained, which implies Holder continuity of solutions. The proof is based on a careful analysis of the associated stochastic flow of characteristics.

• 出版日期2013-3-15