3D Navier-Stokes and Euler equations with initial data characterized by uniformly large vorticity
By A. Babin, A. Mahalov, B. Nicolaenko. 2001
166 citations recorded by the source corpus.
Subfields: Applied Mathematics, Computational Mechanics
View Paper: https://www.semanticscholar.org/paper/5dd417722e731e383705adbc257793119a143070
How researchers see this paper
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In Applied Mathematics
- Yoshikazu Giga
- Jürgen Saal
- Matthias Hieber
- Yoshihiro Shibata
- Jacques Vanneste
- Thomas Y. Hou
- Jian Deng
- Xinwei Yu
In Computational Mechanics
- Jürgen Saal
- Matthias Hieber
- Jacques Vanneste
- Yoshihiro Shibata
- Thomas Y. Hou
- Xinwei Yu
- Okihiro Sawada
- Yoshikazu Giga
Citations in the corpus
- The Navier-Stokes Equations in ℝn with Linearly Growing Initial Data (2005, background): “Babin, Mahalov & Nicolaenko [3, 4] proved the existence of a local mild solution to (1.”
- Uniform global solvability of the rotating Navier-Stokes equations for nondecaying initial data (2008, background): “The global existence for small initial data whose smallness is uniform in Ω is known for periodic initial data ([1], [2]).”
- Uniform Local Solvability for the Navier-Stokes Equations with the Coriolis Force (2005, background): “(ii) Since σ(S) is skew-symmetric ([1], [3]), exp(σ(S)t) is an unitary matrix so |exp σ(S)t| = 1 as a matrix.”
- Geometric Properties and Nonblowup of 3D Incompressible Euler Flow (2004, background): “Much effort has been made to answer this question; see, e.g., Beale et al. (1984), Ebin et al. (1970), Caflisch (1993), Constantin et al. (1996), Tadmor (2001), and Babin (2001).”
- Balance and Spontaneous Wave Generation in Geophysical Flows (2013, methodology): “This is captured by averaging the PEs over the fast IGWs time scale to obtain slow equations which govern both the balanced motion and the amplitude (but not the phase) of IGWs (Embid & Majda 1996, 1998, Majda & Embid 1998, Babin et al. 2000, 2001, 2002, Wirosoetisno et al. 2002).”
- The Fujita–Kato approach to the Navier–Stokes equations in the rotational framework (2010, background): “1) allows a global mild solution for arbitrary large data in the L2-setting provided the speed of rotation is fast enough, see [1–3].”