一维稳态量子Navier-Stokes方程组分析

Abstract

Abstract:

The steady-state quantum Navier-Stokes equations in one space dimension are studied. The existence of classical solutions is proved under the boundary conditions more generalized than that of [Dong J. Classical solutions to
one-dimensional stationary quantum Navier-Stokes equations. J Math Pures Appl, 2011, 96: 521--526]. In addition, the uniqueness of the solutions is investigated under some assumptions. The proofs are based on a reformulation of the problem as a fourth-order elliptic equation by using an exponential variable transformation.

Key words: Quantum Navier-Stokes equations, Stationary solutions, Existence, Uniqueness

CLC Number:

35J40

DONG Jian-Wei, ZHANG You-Lin, WANG Yan-Ping. Analysis of the Stationary Quantum Navier-Stokes Equations in one Space Dimension[J].Acta mathematica scientia,Series A, 2013, 33(4): 719-727.

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References

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Analysis of the Stationary Quantum Navier-Stokes Equations in one Space Dimension

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