LARGE TIME BEHAVIOR OF GLOBAL STRONG SOLUTIONS TO A TWO-PHASE MODEL WITH A MAGNETIC FIELD

doi:10.1007/s10473-022-0512-2

Abstract

Abstract: In this paper, the Cauchy problem for a two-phase model with a magnetic field in three dimensions is considered. Based on a new linearized system with respect to (c - c_∞, P - P_∞, u, H) for constants c_∞ ≥ 0 and P_∞ > 0, the existence theory of global strong solution is established when the initial data is close to its equilibrium in three dimensions for the small H² initial data. We improve the existence results obtained by Wen and Zhu in [40] where an additional assumption that the initial perturbations are bounded in L¹-norm was needed. The energy method combined with the low-frequency and high-frequency decomposition is used to derive the decay of the solution and hence the global existence. As a by-product, the time decay estimates of the solution and its derivatives in the L²-norm are obtained.

Key words: two-phase model, magnetic field, strong solution, global existence, decay rates

CLC Number:

76T10

Wenjun WANG, Zhen CHENG. LARGE TIME BEHAVIOR OF GLOBAL STRONG SOLUTIONS TO A TWO-PHASE MODEL WITH A MAGNETIC FIELD[J].Acta mathematica scientia,Series B, 2022, 42(5): 1921-1946.

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