论文标题
关于具有历史依赖性非线性的广义雷利 - 斯托克斯方程的全球可溶性和规律性
On global solvability and regularity for generalized Rayleigh-Stokes equations with history-dependent nonlinearities
论文作者
论文摘要
我们关注的是由广义雷利 - 斯托克斯方程所控制的初始价值问题，在该方程中，非线性取决于历史状态，并以负顺序的希尔伯特量表为单位。通过使用固定点参数和分数Sobolev空间的嵌入来证明解决方案的可溶性和Hölder规律性。给出了相关逆源问题的应用。
We are concerned with the initial value problem governed by generalized Rayleigh-Stokes equations, where the nonlinearity depends on history states and takes values in Hilbert scales of negative order. The solvability and Hölder regularity of solutions are proved by using fixed point arguments and embeddings of fractional Sobolev spaces. An application to a related inverse source problem is given.
