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Existence ‘in the large’ of a solution to primitive equations in a domain with uneven bottom
Published/Copyright:
January 25, 2010
Abstract
The existence and uniqueness theorems ‘in the large’ are proved for a system of primitive equations in the Cartesian coordinates in a domain with an uneven bottom. The original equations are slightly modified: some terms containing mixed derivatives are omitted because they are small. Namely, it is proved that for arbitrary time period [0,T] in a spatial domain Ω = {(x,y,z) | (x,y) ∈ Ω′, z ∈ [0,H(x,y)]}, for an arbitrary viscosity coefficients ν,ν1 > 0, any depth H ∈ C2(Ω′), H ⩾ H0 > 0, and any initial conditions 
there exists a unique weak solution 
and the norms 
are continuous with respect to t, where s is the vertical variable.
Published Online: 2010-01-25
Published in Print: 2009-December
© de Gruyter 2009
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Articles in the same Issue
- Existence ‘in the large’ of a solution to primitive equations in a domain with uneven bottom
- Uzawa method on semi-staggered grids for unsteady Bingham media flows
- Methods of numerical analysis for boundary value problems with strong singularity
- Constructive and formal difference schemes for singularly perturbed parabolic equations in unbounded domains in the case of solutions growing at infinity
Articles in the same Issue
- Existence ‘in the large’ of a solution to primitive equations in a domain with uneven bottom
- Uzawa method on semi-staggered grids for unsteady Bingham media flows
- Methods of numerical analysis for boundary value problems with strong singularity
- Constructive and formal difference schemes for singularly perturbed parabolic equations in unbounded domains in the case of solutions growing at infinity
