无变形扩散的非等温磁粘弹性流体的全局解
Global solutions for non-isothermal magnetoviscoelastic fluids in the absence of deformation diffusion
- The University of Alabama（阿拉巴马大学）
- Vanderbilt University（范德堡大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该论文研究非等温不可压缩磁粘弹性流体的全局解，通过引入结合速度与逆变形张量的辅助变量揭示耗散结构，证明了小扰动下强解的全局存在性。
AI中文摘要：
我们研究了在 $\mathbb{R}^N$（$N=2,3$）中不可压缩磁粘弹性流体的非等温模型，该模型将不可压缩 Navier-Stokes 方程与变形张量、温度和磁化的演化方程耦合。材料系数允许依赖于温度，并且对变形张量不施加人工扩散，从而形成一个耦合的双曲-抛物系统。我们为足够正则的初始数据建立了强解的局部适定性，并证明了常数平衡态小扰动的全局存在性。全局分析依赖于一个合适的辅助变量，该变量结合了速度和逆变形张量，揭示了隐藏的耗散结构，并使我们能够为耦合系统推导出一致的高阶能量估计。
英文摘要：
We study a non-isothermal model for incompressible magnetoviscoelastic fluids in $\mathbb{R}^N$, $N=2,3$, coupling the incompressible Navier-Stokes equations with the evolution equations for the deformation tensor, temperature, and magnetization. The material coefficients are allowed to depend on the temperature, and no artificial diffusion is imposed on the deformation tensor, leading to a coupled hyperbolic-parabolic system. We establish local well-posedness of strong solutions for sufficiently regular initial data and prove global existence for small perturbations of a constant equilibrium. The global analysis relies on a suitable auxiliary variable combining the velocity and the inverse deformation tensor, which reveals a hidden dissipative structure and allows us to derive uniform higher-order energy estimates for the coupled system.
