In this paper, we are interested in proving the existence of a weak martingale solution of the stochastic smectic-A liquid crystal system driven by a pure jump noise in both 2D and 3D bounded domains. We prove the existence of a global weak martingale solution under some non-Lipschitz assumptions on the coefficients. The construction of the solution is based on a Faedo–Galerkin approximation, a compactness method and the Skorokhod representation theorem. In the two-dimensional case, we prove the pathwise uniqueness of the weak solution, which implies the existence of a unique probabilistic strong solution.

中文翻译：

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具有跳跃型乘性噪声的随机近晶A液晶模型的鞅解

在本文中，我们有兴趣证明在 2D 和 3D 有界域中由纯跳跃噪声驱动的随机 smectic-A 液晶系统的弱鞅解的存在。我们证明了在系数的一些非 Lipschitz 假设下存在全局弱鞅解。解决方案的构建基于 Faedo-Galerkin 近似、紧致性方法和 Skorokhod 表示定理。在二维情况下，我们证明了弱解的路径唯一性，这意味着存在唯一的概率强解。