Von Karman Equations Without Rotational Inertia
This chapter treats well-posedness of solutions to von Karman models that do not account for rotational terms. The absence of rotational inertia terms raises several questions related to generation of well-posed flows, making the subject more challenging. This is due to the lack of regularizing effect on the velocity s expressed by the term αΔ u tt in (3.1.1). In fact, in the absence of this term the issue of uniqueness of finite energy solutions has been an open problem in the literature. It turns out that the key to solvability of this problem is sharp regularity of Airy’s stress function (see Corollary 1.4.5). In fact, this sharp regularity property allows us to use abstract results formulated in Chapter 2. The proof of well-posedness for the model without rotational forces follows from the abstract results in Theorems 2.4.5 and 2.4.16.
KeywordsGeneralize Solution Weak Solution Strong Solution Rotational Inertia Free Boundary Condition
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