Low Mach number limit of a compressible micropolar fluid model

Zero dissipation limit to rarefaction wave with vacuum for the micropolar compressible flow with temperature‐dependent transport coefficients

“…Later, Cui and Yin 4 studied the stability of the composite wave for the inflow problem on the micropolar fluid model, Jin and Duan 5 verified the stability of rarefaction waves for 1D compressible viscous micropolar fluid model. Recently, Duan 6 proved the global solutions for the one‐dimensional with zero heat conductivity case, and Su verified the global existence and low Mach number limit of a compressible micropolar fluid in other studies 7,8 For multidimensional case, Mujakovi et al 9‐13 considered the three‐dimensional spherical symmetry solution and derived its local existence, global existence, uniqueness, and large time behavior.…”

Strong solutions to the three-dimensional barotropic compressible magneto-micropolar fluid equations with vacuum

“…The theory of micropolar fluids introduced by Eringen in the 1960s (see [10,11]) is a significant step toward the generalization of the classical Navier-Stokes model. Due to the profound physical background and important mathematical significance, the compressible micropolar fluid equations have been extensively studied, such as large time behavior of solutions [14,15,22], blow-up criterion of solutions [4,5], qualitative theory of symmetric solutions [7][8][9]17], low Mach number limit of solutions [18,19], and so on. By constructing global weak solutions as limits of smooth solutions, Chen et al [6] proved global existence of weak solutions to the three-dimensional compressible micropolar fluid system with initial data which may be discontinuous and may contain vacuum states.…”

Inviscid incompressible limits for rotating fluids

“…For further results on weak and strong solutions to the micropolar system we also refer to [1], [6], [7] [11], [12], [13], [20], [25], [40], [41] and references therein. In particular, in the context of singular limit analysis, recent results are given in [35], [36], [37].…”

“…In the last years, the study of the low Mach number and/or inviscid regime for compressible fluids has been of large interest for many authors (see [23] and references therein). However, in the context of micro-polar compressible fluids very few results are present (see [35], [36], [37]). Indeed, as far as the author is aware, the weak-weak convergence in the low Mach number limit for the compressible (barotropic) micro-polar fluid in the whole space with ill-prepared initial data has not been analyzed before.…”