On the spectral dynamics of the deformation tensor and new a priori estimates for the 3D Euler equations
نویسنده
چکیده
In this paper we study the dynamics of eigenvalues of the deformation tensor for solutions of the 3D incompressible Euler equations. Using the evolution equation of the L2 norm of spectra, we deduce new a priori estimates of the L2 norm of vorticity. As an immediate corollary of the estimate we obtain a new sufficient condition of L2 norm control of vorticity. We also obtain decay in time estimates of the ratios of the eigenvalues. In the remarks we discuss what these estimates suggest in the study of searching initial data leading to a possible finite time singularities. We find that the dynamical behaviors of L2 norm of vorticity are controlled completely by the second largest eigenvalue of the deformation tensor. AMS Subject Classification Number: 35Q35, 76B03 ∗Permanent Address: Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea, e-mail : [email protected]
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