Global existence and asymptotic behavior of strong solutions to three dimensional modified primitive equations with Caputo fractional time derivatives

A three dimensional system of globally modified fractional viscous primitive equations with Caputo fractional time derivatives, is developed and analyzed. To investigate the asymptotic behavior of strong solutions, the modifying factors FN(‖v‖W1,2(1+2ε)1+2ε) and FN(‖v‖W1,2(1+2ε)1+2ε+‖T‖W1,2(1+2ε)1+2ε) are introduced into the time fractional primitive equations. The global existence of strong solutions is established for the globally modified time fractional primitive equations. Subsequently, the existence and uniqueness of local (or global) strong solutions to the time fractional primitive equations are presented for any (or small) initial data and external force, in which we do not add any modifying factor on the nonlinear terms. Then after constructing a positively invariant absorbing set, we show the existence of a global attracting set for the globally modified time fractional primitive equations.