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| On Mixed Pressure-Velocity Regularity Criteria to the Navier-stokes Equations in Lorentz Spaces, Part II: The Non-slip Boundary Value Problem* |
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Citation： |
Hugo BEIRA˜O DA VEIGA,Jiaqi YANG.On Mixed Pressure-Velocity Regularity Criteria to the Navier-stokes Equations in Lorentz Spaces, Part II: The Non-slip Boundary Value Problem*[J].Chinese Annals of Mathematics B,2022,43(1):51~58 |
| Page view： 432
Net amount： 593 |
Authors： |
Hugo BEIRA?O DA VEIGA; Jiaqi YANG |
Foundation： |
Funda?c?ao para a Ci?encia e a Tecnologia of Portugal (No. UIDB/MAT/04561/2020) and the National Natural Science Foundation of China (No. 12001429). |
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| Abstract： |
This paper is a continuation of the authors recent work [Beir?ao da Veiga, H.and Yang, J., On mixed pressure-velocity regularity criteria to the Navier-Stokes equations in Lorentz spaces, Chin. Ann. Math., 42(1), 2021, 1–16], in which mixed pressure-velocity criteria in Lorentz spaces for Leray-Hopf weak solutions of the three-dimensional NavierStokes equations, in the whole space R3 and in the periodic torus T3 , are established. The purpose of the present work is to extend the result of mentioned above to smooth, bounded domains ?, under the non-slip boundary condition. Let π denote the fluid pressure and v the fluid velocity. It is shown that if π/(1+π|v|)θ ∈ Lp (0, T ;L(?)), where 0 ≤ θ ≤ 1, and 2/p + 3/q = 2 ? θ with p ≥ 2, then v is regular on ? × (0, T ]. |
Keywords： |
Navier-Stokes equations, Pressure-speed links, Regularity criteria,Lorentz spaces, Boundary value problem |
Classification： |
35Q30, 76D03, 76D05 |
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