Higher Regularity of a Coupled Parabolic-Hyperbolic Fluid-Structure Interactive System
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George Avalos
Abstract
This paper considers an established model of a parabolic-hyperbolic coupled system of two PDEs, which arises when an elastic structure is immersed in a fluid. Coupling occurs at the interface between the two media. Semigroup well-posedness on the space of finite energy for {𝑤, 𝑤𝑡, 𝑢} was established in [Contemp. Math. 440: 15–54, 2007]. Here, [𝑤, 𝑤𝑡] are the displacement and the velocity of the structure, while 𝑢 is the velocity of the fluid. The domain D(A) of the generator A does not carry any smoothing in the 𝑤-variable (its resolvent 𝑅(λ, A) is not compact on this component space). This raises the issue of higher regularity of solutions. This paper then shows that the mechanical displacement, fluid velocity, and pressure terms do enjoy a greater regularity if, in addition to the I.C. {𝑤0, 𝑤1, 𝑢0} ∈ D(A), one also has 𝑤0 in (𝐻2(Ω𝑠))𝑑.
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- Higher Regularity of a Coupled Parabolic-Hyperbolic Fluid-Structure Interactive System
- Impulse Control in Discrete Time
- Mixed and Crack-Type Boundary Value Problems in Mindlin's Theory of Piezoelectricity
- Estimates of the Location of a Free Boundary for the Obstacle and Stefan Problems Obtained by Means of Some Energy Methods
- Extended Normal Vector Field and the Weingarten Map on Hypersurfaces
- Capacity Induced by a Nonlinear Operator and Applications
- Boundary Layers for the Navier–Stokes Equations. The Case of a Characteristic Boundary
- Large Time Behavior of Solutions to One Nonlinear Integro-Differential Equation
- On One Boundary Value Problem for a Nonlinear Equation with the Iterated Wave Operator in the Principal Part
- On Solvability and Well-Posedness of Boundary Value Problems for Nonlinear Hyperbolic Equations of the Fourth Order
- A Note on the One-Side Exact Boundary Observability for Quasilinear Hyperbolic Systems
- Principle of Exchange of Stabilities and Dynamic Transitions
Articles in the same Issue
- Higher Regularity of a Coupled Parabolic-Hyperbolic Fluid-Structure Interactive System
- Impulse Control in Discrete Time
- Mixed and Crack-Type Boundary Value Problems in Mindlin's Theory of Piezoelectricity
- Estimates of the Location of a Free Boundary for the Obstacle and Stefan Problems Obtained by Means of Some Energy Methods
- Extended Normal Vector Field and the Weingarten Map on Hypersurfaces
- Capacity Induced by a Nonlinear Operator and Applications
- Boundary Layers for the Navier–Stokes Equations. The Case of a Characteristic Boundary
- Large Time Behavior of Solutions to One Nonlinear Integro-Differential Equation
- On One Boundary Value Problem for a Nonlinear Equation with the Iterated Wave Operator in the Principal Part
- On Solvability and Well-Posedness of Boundary Value Problems for Nonlinear Hyperbolic Equations of the Fourth Order
- A Note on the One-Side Exact Boundary Observability for Quasilinear Hyperbolic Systems
- Principle of Exchange of Stabilities and Dynamic Transitions
