Propagation of $L^ q_ k$-smoothness for solutions of the Euler equation
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- by Gustavo Ponce PDF
- Trans. Amer. Math. Soc. 314 (1989), 51-61 Request permission
Abstract:
The motion of an ideal incompressible fluid is described by a system of partial differential equations known as the Euler equation. Considering the initial value problem for this equation, we prove that in a classical solution the $L_k^q$-regularity of the data propagates along the fluid lines. Our method consists of combining properties of the $\varepsilon$-approximate solution with ${L^q}$-energy estimates and simple results of classical singular integral operators. In particular, for the two-dimensional case we present an elementary proof.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 314 (1989), 51-61
- MSC: Primary 35B65; Secondary 35Q10, 76C10
- DOI: https://doi.org/10.1090/S0002-9947-1989-0937250-1
- MathSciNet review: 937250