Strong solutions of the Navier-Stokes equations for isentropic compressible fluids

By Hi Jun Choe, Hyunseok Kim. 2003

256 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1e6576c7bce086804ab894c8caddeb4c2c27cff8

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In Applied Mathematics

1. Jing Li
2. Zhouping Xin
3. Xiangdi Huang
4. Yonggeun Cho
5. Hyunseok Kim
6. Huanyao Wen
7. Changyou Wang
8. Tao Huang

In Control and Systems Engineering

1. Yonggeun Cho
2. Xiangdi Huang
3. Jing Li
4. Hyunseok Kim
5. Hi Jun Choe
6. Zhouping Xin
7. Huanyao Wen
8. Changyou Wang

In Mathematical Physics

1. Jing Li
2. Xiangdi Huang
3. Zhouping Xin
4. Yonggeun Cho
5. Hyunseok Kim
6. Huanyao Wen
7. Hi Jun Choe
8. Changyou Wang

Citations in the corpus

• 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.”
• Strong Solutions of the Navier–Stokes Equations for Nonhomogeneous Incompressible Fluids (2003, background): “For details, please refer to Choe and Kim ( [0000] ).”
• 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].”
• Weak–Strong Uniqueness for the Isentropic Compressible Navier–Stokes System (2008, background): “Weak–strong uniqueness results properly speaking, namely uniqueness results in classes of weak solutions, are found in Desjardins [6] and Choe-Kim [3].”
• 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.”
• Existence results for viscous polytropic fluids with vacuum (2006, background): “Following the ideas in [1, 3], we differentiate (1.”
• Blowup Criterion for Viscous Baratropic Flows with Vacuum States (2010, background): “In the case where the initial density need not be positive and may vanish in an open set, the existence and uniqueness of local strong (or classical) solutions are proved recently in [4–6, 8, 28].”
• 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.”