On the Initial Value Problem for the Basic Equations of Hydrodynamics
نویسندگان
چکیده
Let x = (x1, . . . , xn) denote a point in R , and dx = dx1 dx2 · · · dxn denote the volume element in R . Let u(x, t) : G → R be a time-dependent vector field defined on an open subset Ĝ of x-t-space with components ui, i = 1, . . . , n. G will be called a domain for brevity, though we do not assume that Ĝ is connected. Domains in x-space will be denoted G, in x-t-space they will be denoted Ĝ. A vector field u(x, t) which is C in x on an x-t-domain Ĝ is divergence free if it satisfies the differential equation
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تاریخ انتشار 2006