科研之友
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摘要
Two new time-dependent versions of div-curl results in a bounded domain Omega subset of R-3 are presented. We study a limit of the product v(k)w(k), where the sequences v(k) and w(k) belong to L-2(Omega). In Theorem 2.1 we assume that del x v(k) is bounded in the L-p-norm and del . w(k) is controlled in the L-r-norm. In Theorem 2.2 we suppose that del x w(k) is bounded in the L-p-norm and del . w(k) is controlled in the L-r-norm. The time derivative of w(k) is bounded in both cases in the norm of H-1(Omega). The convergence (in the sense of distributions) of v(k)w(k) to the product vw of weak limits of v(k) and w(k) is shown.
- 出版日期2010
