• an h1 setting for the navier–stokes equations: quantitative estimates

    جزئیات بیشتر مقاله
    • تاریخ ارائه: 1390/01/01
    • تاریخ انتشار در تی پی بین: 1390/01/01
    • تعداد بازدید: 340
    • تعداد پرسش و پاسخ ها: 0
    • شماره تماس دبیرخانه رویداد: -
    we consider the incompressible navier–stokes (ns) equations on a torus, in the setting of the spaces l2 and h1; our approach is based on a general framework for semi-linear or quasi-linear parabolic equations proposed in the previous work (morosi and pizzocchero (2008) [5]).wepresent some estimates on the linear semigroup generated by the laplacian and on the quadratic ns nonlinearity; these are fully quantitative, i.e., all the constants appearing therein are given explicitly. as an application we show that, on a three-dimensional torus t3, the (mild) solution of the ns cauchy problem is global for each h1 initial datum u0 with zero mean, such that ‖curl u0‖l2 0.407; this improves the bound for global existence ‖curl u0‖l2 0.00724, derived recently by robinson and sadowski (2008) [3]. we announce some future applications, based again on the h1 framework and on the general scheme of [5].

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