GLOBAL CLASSICAL SOLUTIONS TO THE 3D CAUCHY PROBLEM OF COMPRESSIBLE MAGNETO-MICROPOLAR FLUID EQUATIONS WITH FAR FIELD VACUUM

This paper concerns the three-dimensional Cauchy problem of compressible isentropic magneto-micropolar fluid equations with initial density containing vacuum states. Based on energy method and the structural characteristics of the model, we show the global existence of classical solutions provided that [(gamma- 1)(1/ a) + nu- (1/4) ]E-0 is suitably small, where gamma, nu, and E0 represent the adiabatic exponent, resistivity coefficient, and initial energy, respectively. Our result is an extension of the work of Wei-Guo-Li (J. Differential Equations, 263: 2457-2480, 2017), where the global existence of smooth solutions was established under the condition that the initial data are small perturbations of some given constant state.

Automated summary

This paper deals with the three-dimensional Cauchy problem of compressible isentropic magneto-micropolar fluid equations with initial density containing vacuum states. By using energy method and the structural characteristics of the model, the global existence of classical solutions is shown under the condition that [(γ-1)(1/a) + ν - (1/4)]E0 is suitably small, where γ, ν, and E0 represent the adiabatic exponent, resistivity coefficient, and initial energy, respectively. This result extends the work of Wei-Guo-Li (J. Differential Equations, 263: 2457-2480, 2017), where the global existence of smooth solutions was established under the condition that the initial data are small perturbations of some given constant state.