Continuous Dependence on the Heat Source of 2D Large-Scale Primitive Equations in Oceanic Dynamics

Abstract

In this paper, we consider the initial-boundary value problem for the two-dimensional primitive equations of the large-scale oceanic dynamics. These models are often used to predict weather and climate change. Using the differential inequality technique, rigorous a priori bounds of solutions and the continuous dependence on the heat source are established. We show the application of symmetry in mathematical inequalities in practice.

Spatial Decay Estimates and Continuous Dependence for the Oldroyd Fluid

“…When a small disturbance occurs in the viscosity coefficient, we study what kind of disturbance will occur in the solutions of the equation. In past decades, studies on structural stability have received a lot of attention, and a large number of papers have emerged, including those of Liu and Zheng [17], Avalos and Lesiecka [18], Meyvacı [19], Quintanilla [1,20,21], Liu et al [22][23][24][25][26], Hameed and Harfash [27], Scott et al [28,29], Li et al [30][31][32][33], Ciarletta and Straughan [34], and Franchi and Straughan [35]. Straughan [1] proved that Kelvin-Voigt fluid depended continuously on the coefficients of the fluid.…”

Special Issue Editorial “Symmetry in the Mathematical Inequalities”

“…Y. Li and P. Zeng, in the paper "Continuous Dependence on the Heat Source of 2D Large-Scale Primitive Equations in Oceanic Dynamics" [10], studied the initial boundary value problem for the two-dimensional primitive equations of large-scale oceanic dynamics. These models are often used to predict the weather and climate change.…”

Structural Stability on the Boundary Coefficient of the Thermoelastic Equations of Type III

“…β is the cooling coefficient. For more papers of the type, one can refer to [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. However, these results above only considered the case of the bounded region.…”

“…u, ∇u, θ, ∇θ → 0, as x 3 → ∞, (11) with the initial-boundary conditions u(x, 0) = u t (x, 0) = 0, x ∈ R, t > 0, (12) θ(x, 0) = θ t (x, 0) = 0, x ∈ R, t > 0,…”