A Uniqueness Result for the Navier-Stokes Equations with Vanishing Vertical Viscosity
نویسنده
چکیده
Chemin et al. [M2AN Math. Model. Numer. Anal., 34 (2000), pp. 315–335.] considered the three-dimensional Navier–Stokes equations with vanishing vertical viscosity. Assuming that the initial velocity is square-integrable in the horizontal direction and Hs in the vertical direction, they prove existence of solutions for s > 1/2 and uniqueness of solutions for s > 3/2. Here, we close the gap between existence and uniqueness, proving uniqueness of solutions for s > 1/2. Standard techniques are used.
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ورودعنوان ژورنال:
- SIAM J. Math. Analysis
دوره 33 شماره
صفحات -
تاریخ انتشار 2002