乘性高斯噪声驱动下随机惩罚双折射液晶模型的强解
Strong solution to stochastic penalised nematic liquid crystals model driven by multiplicative Gaussian noise
摘要：
本文证明了在乘性高斯噪声驱动下，二维和三维惩罚双折射液晶的随机系统存在唯一的极大局部强解。作为我们研究的一个副产品，但独立的兴趣，我们提出了一个一般的方法，基于不动点的论点，建立一个抽象的随机发展方程的系数满足局部利普希茨条件涉及两个不同的巴拿赫空间的范数的最大局部解的存在性和唯一性。
英文摘要：
In this paper, we prove the existence of a unique maximal local strong solutions to a stochastic system for both 2D and 3D penalised nematic liquid crystals driven by multiplicative Gaussian noise. In the 2D case, we show that this solution is global.As a by-product of our investigation, but of independent interest, we present a general method based on fixed point arguments to establish the existence and uniqueness of a maximal local solution of an abstract stochastic evolution equations with coefficients satisfying local Lipschitz condition involving the norms of two different Banach spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
