Unique solvability of the initial boundary value problems for compressible viscous fluids

By Yonggeun Cho, Hi Jun Choe, Hyunseok Kim. 2004

452 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/53e5f170ecdaa2dcc779758ad903a4d07fb5ace1

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Existence results for viscous polytropic fluids with vacuum (2006, background): “Hence by virtue of the elliptic regularity result in [1], we deduce that |∇(wk − v)(t)|H1 ≤ C ( |divgk(t)− divg(t)|L2 + |wk(t)− v(t)|D1 0 )”
Strong solutions of the compressible nematic liquid crystal flow (2011, methodology): “8), has been previously established by Choe-Kim [4] and Cho-Choe-Kim [3].”
Relative Entropies, Suitable Weak Solutions, and Weak-Strong Uniqueness for the Compressible Navier–Stokes System (2011, background): “[2] Y. Cho, H.J. Choe, and H. Kim.”
On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities (2006, methodology): “10), we follow the arguments in [2, 3, 4]; we first apply the standard inequalities such as Hölder, Sobolev and Young’s inequalities and then use Lemma 3.”
Dissipative measure-valued solutions to the compressible Navier–Stokes system (2015, background): “Cho, Choe and Kim [4], Valli and Zaja̧czkowski [32].”
A Beale-Kato-Majda Blow-up criterion for the 3-D compressible Navier-Stokes equations (2010, methodology): “When the initial vaccuum is allowed, the local well-posedne ss and blowup criterion for strong solutions to the compressible Navie r-Stokes equations were established in a series of papers [7, 8, 9] by Cho, C e and Kim.”
Some uniform estimates and blowup behavior of global strong solutions to the Stokes approximation equations for two-dimensional compressible flows (2006, background): “As emphasized in many papers related to compressible fluid dynamics [2], [7], [9]-[11], [21], [22], [24]-[26], the possible appearance of vacuum and uniform upper bound estimate on the density is one of the major difficulties when trying to prove global existence and strong regularity results.”
Weak–Strong Uniqueness for the Isentropic Compressible Navier–Stokes System (2008, background): “Cho, Choe and Kim [2] were able to deal with data with vanishing density.”
Vanishing of Vacuum States and Blow-up Phenomena of the Compressible Navier-Stokes Equations (2008, background): “As emphasized in many papers related to compressible fluid dynamics [9,10,18,20,21,24,27,45,46,48,50,52], the possible appearance of vacuum is one of the major difficulties when trying to prove global existence and strong regularity results.”
Global well‐posedness of classical solutions with large oscillations and vacuum to the three‐dimensional isentropic compressible Navier‐Stokes equations (2010, background): “For the multi-dimensional case, the local existence and uniqueness of classical solutions are known in [23, 28] in the absence of vacuum and recently, for strong solutions also, in [2, 4, 5, 25] for the case that the initial density need not be positive and may vanish in open sets.”