On the Singular p-Laplacian System Under Navier Slip Type Boundary Conditions: The Gradient-Symmetric Case

Veiga, H. Beirão da

doi:10.1007/978-3-0348-0939-9_6

Recent Developments of Mathematical Fluid Mechanics

2016

DOI: 10.1007/978-3-0348-0939-9_6

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On the Singular p-Laplacian System Under Navier Slip Type Boundary Conditions: The Gradient-Symmetric Case

H. Beirão da Veiga

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2024

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Remark on the Local Well-Posedness of Compressible Non-Newtonian Fluids with Initial Vacuum

Al Baba,

Al Taki,

Hussein

2024

J. Math. Fluid Mech.

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We discuss in this short note the local-in-time strong well-posedness of the compressible Navier–Stokes system for non-Newtonian fluids on the three dimensional torus. We show that the result established recently by Kalousek, Mácha, and Nečasova in https://doi.org/10.1007/s00208-021-02301-8 can be extended to the case where vanishing density is allowed initially. Our proof builds on the framework developed by Cho, Choe, and Kim in https://doi.org/10.1016/j.matpur.2003.11.004 for compressible Navier–Stokes equations in the case of Newtonian fluids. To adapt their method, special attention is given to the elliptic regularity of a challenging nonlinear elliptic system. We show particular results in this direction, however, the main result of this paper is proven in the general case when elliptic $$W^{2,p}$$ W 2 , p -regularity is imposed as an assumption. Also, we give a finite time blow-up criterion.

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Remark on the Local Well-Posedness of Compressible Non-Newtonian Fluids with Initial Vacuum

Al Baba,

Al Taki,

Hussein

2024

J. Math. Fluid Mech.

View full text Add to dashboard Cite

show abstract

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On the Singular p-Laplacian System Under Navier Slip Type Boundary Conditions: The Gradient-Symmetric Case

Cited by 1 publication

References 18 publications

Remark on the Local Well-Posedness of Compressible Non-Newtonian Fluids with Initial Vacuum

Remark on the Local Well-Posedness of Compressible Non-Newtonian Fluids with Initial Vacuum

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