源于血管中血栓生物力学多尺度建模的相场系统：二维情形的局部适定性
A phase-field system arising from multiscale modeling of thrombus biomechanics in blood vessels: local well-posedness in dimension two
AI总结：
研究描述血流与血栓相互作用的相场模型，在二维情形下证明了强解的局部存在性与唯一性，并验证了序参量的严格分离性。
摘要：
我们考虑一个描述血流与血栓之间相互作用的相场模型。后者被假定是一种粘弹性材料。描述混合物内聚能的势能被假定为Flory-Huggins类型（即对数型）。这确保了耗散能的下有界性。在二维情形下，只要纯流体相的两个粘度足够接近，我们证明了强解的局部（时间）存在性和唯一性。我们还证明了，如果序参量在初始时刻严格分离于纯相，则它将始终保持这种严格分离状态。
英文摘要：
We consider a phase-field model which describes the interactions between the blood flow and the thrombus. The latter is supposed to be a viscoelastic material. The potential describing the cohesive energy of the mixture is assumed to be of Flory-Huggins type (i.e. logarithmic). This ensures the boundedness from below of the dissipation energy. In the two dimensional case, we prove the local (in time) existence and uniqueness of a strong solution, provided that the two viscosities of the pure fluid phases are close enough. We also show that the order parameter remains strictly separated from the pure phases if it is so at the initial time.
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