随机三阶流体方程的适定性
Well-posedness of stochastic third grade fluid equation
摘要：
本文建立了三阶流体方程在乘性白噪声扰动下的适定性。该方程描述了具有相关粘弹性性质的微分型非牛顿流体的运动。我们面对的是一个强非线性随机偏微分方程，附加了Navier滑移边界条件。在索伯列夫空间H^2中取初始条件，证明了在二维非轴对称有界区域上强解（概率意义下）的存在唯一性.
英文摘要：
In this paper, we establish the well-posedness for the third grade fluid equation perturbed by a multiplicative white noise. This equation describes the motion of a non-Newtonian fluid of differential type with relevant viscoelastic properties. We are faced with a strongly nonlinear stochastic partial differential equation supplemented with a Navier slip boundary condition. Taking the initial condition in the Sobolev space H^2, we show the existence and the uniqueness of the strong (in the probability sense) solution in a two dimensional and non axisymmetric bounded domain.
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