Details

Autor(en) / Beteiligte

• Sun, Jinyi
• Cui, Shangbin

Titel

Sharp well-posedness and ill-posedness of the three-dimensional primitive equations of geophysics in Fourier–Besov spaces

Ist Teil von

• Nonlinear analysis: real world applications, 2019-08, Vol.48, p.445-465

Ort / Verlag

Amsterdam: Elsevier Ltd

Erscheinungsjahr

2019

Quelle

Elsevier ScienceDirect Journals

Beschreibungen/Notizen

• We study the well-posedness and ill-posedness for the Cauchy problem of the three-dimensional primitive equations describing the large-scale oceanic and atmospheric circulations. By using the Littlewood–Paley analysis technique, we prove that the Cauchy problem of the three-dimensional primitive equations with the Prandtl number P=1 is locally well-posed in the Fourier–Besov spaces FḂp,r2−3p(R3) for 1<p≤∞,1≤r<∞ and FḂ1,r−1(R3) for 1≤r≤2, and is globally well-posed in these spaces when the initial data are small. We also verify that such problem is ill-posed in FḂ1,r−1(R3) for 2<r≤∞, which implies that our work completes a dichotomy of well-posedness and ill-posedness for the three-dimensional primitive equations in the Fourier–Besov space framework.