### Electronic Research Archive

2020, Issue 2: 691-719. doi: 10.3934/era.2020036
Special Issues

# The well-posedness and regularity of a rotating blades equation

• Received: 01 January 2020 Revised: 01 March 2020
• Primary: 35A01, 35D30; Secondary: 35L76, 35Q74

• In this paper, a rotating blades equation is considered. The arbitrary pre-twisted angle, arbitrary pre-setting angle and arbitrary rotating speed are taken into account when establishing the rotating blades model. The nonlinear PDEs of motion and two types of boundary conditions are derived by the extended Hamilton principle and the first-order piston theory. The well-posedness of weak solution (global in time) for the rotating blades equation with Clamped-Clamped (C-C) boundary conditions can be proved by compactness method and energy method. Strong energy estimates are derived under additional assumptions on the initial data. In addition, the existence and regularity of weak solutions (global in time) for the rotating blades equation with Clamped-Free (C-F) boundary conditions are proved as well.

Citation: Lin Shen, Shu Wang, Yongxin Wang. The well-posedness and regularity of a rotating blades equation[J]. Electronic Research Archive, 2020, 28(2): 691-719. doi: 10.3934/era.2020036

### Related Papers:

• In this paper, a rotating blades equation is considered. The arbitrary pre-twisted angle, arbitrary pre-setting angle and arbitrary rotating speed are taken into account when establishing the rotating blades model. The nonlinear PDEs of motion and two types of boundary conditions are derived by the extended Hamilton principle and the first-order piston theory. The well-posedness of weak solution (global in time) for the rotating blades equation with Clamped-Clamped (C-C) boundary conditions can be proved by compactness method and energy method. Strong energy estimates are derived under additional assumptions on the initial data. In addition, the existence and regularity of weak solutions (global in time) for the rotating blades equation with Clamped-Free (C-F) boundary conditions are proved as well.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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