THE PRIMITIVE EQUATIONS IN THE SCALING INVARIANT SPACE L∞ (L1)

DOI IR IR (HANDLE) Open Access

Description

Consider the primitive equations on R2 ×(z0, z1) with initial data a of the form a = a1 +a2, where a1 ∈ BUCσ(R2; L1(z0, z1)) and a2 ∈ L∞σ (R2; L1(z0, z1)) and where BUCσ(L1) and L∞σ (L1) denote the space of all solenoidal, bounded uniformly continuous and all solenoidal, bounded functions on R2, respectively, which take values in L1 (z0, z1). These spaces are scaling invariant and represent the anisotropic character of these equations. It is shown that, if ka2kL∞σ (L1) is sufficiently small, then this set of equations has a unique, local, mild solution. If in addition a is periodic in the horizontal variables, then this solution is a strong one and extends to a unique, global, strong solution. The primitive equations are thus strongly and globally well-posed for these data. The approach depends crucially on mapping properties of the hydrostatic Stokes semigroup in the L∞(L1)-setting and can thus be seen as the counterpart of the classical iteration schemes for the Navier-Stokes equations for the situation of the primitive equations

Journal

Keywords

Details 詳細情報について

Report a problem

Back to top