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Regularity Criteria of Axisymmetric Weak Solutions to the 3D Magnetohydrodynamic Equations
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作者 Bao-quan YUAN Feng-ping LI 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2013年第2期289-302,共14页
In this paper, we study the regularity criteria for axisymmetric weak solutions to the MHD equa- tions in R3. Let we, Jo and ue be the azimuthal component of w, J and u in the cylindrical coordinates, respectively. Th... In this paper, we study the regularity criteria for axisymmetric weak solutions to the MHD equa- tions in R3. Let we, Jo and ue be the azimuthal component of w, J and u in the cylindrical coordinates, respectively. Then the axisymmetric weak solution (u,b) is regular on (0, T) if (wo,Jo) E Lq(O,T;Lp) or (oae,V(uoeo)) e Lq(0,T;Lp) with 3 + 2 〈 2, 3 〈 p 〈 oo. In the endpoint case, one needs conditions (we, Jo) C LI(0, T;B∞∞) or (wo, V(uoeo)) C LI(0, T;B ∞∞). 展开更多
关键词 regularity criteria axisymmetric solutions Besov space
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Simplified method for predicating consolidation settlement of soft ground improved by floating soil-cement column 被引量:12
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作者 龚晓南 田效军 胡文韬 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第7期2699-2706,共8页
A simplified method is presented for predicting consolidation settlement of soft ground improved by floating soil-cement column on the basis of double soil-layer consolidation theory. Combining the axisymmetric consol... A simplified method is presented for predicting consolidation settlement of soft ground improved by floating soil-cement column on the basis of double soil-layer consolidation theory. Combining the axisymmetric consolidation model and equal strain assumption, the governing equation was derived for the consolidation of clayey subsoil reinforced by soil-cement column. By modifying the boundary condition of the interface between the improved layer and underlying layer on seepage and pore-water pressure, the analytical solution of consolidation of soft ground improved by floating soil-cement column was developed under depth-dependent ramp load. The results of the parameter analysis of consolidation behavior show that the consolidation rate is closely related with the depth replacement ratio by the column and the permeability of upper layer. The influence of column-soil constrained modulus ratio and radius ratio of the influence zone to the column on consolidation is also affected by depth replacement ratio. The column-soil total stress ratio increases with time and approaches the final value accompanied with the dissipation of excess pore water pressure. 展开更多
关键词 axisymmetric consolidation model floating soil-cement column consolidation depth-dependent ramp load analytical solution
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Global axisymmetric classical solutions of full compressible magnetohydrodynamic equations with vacuum free boundary and large initial data
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作者 Kunquan Li Zilai Li Yaobin Ou 《Science China Mathematics》 SCIE CSCD 2022年第3期471-500,共30页
In this paper,the global existence of the classical solution to the vacuum free boundary problem of full compressible magnetohydrodynamic equations with large initial data and axial symmetry is studied.The solutions t... In this paper,the global existence of the classical solution to the vacuum free boundary problem of full compressible magnetohydrodynamic equations with large initial data and axial symmetry is studied.The solutions to the system(1.6)–(1.8) are in the class of radius-dependent solutions,i.e.,independent of the axial variable and the angular variable.In particular,the expanding rate of the moving boundary is obtained.The main difficulty of this problem lies in the strong coupling of the magnetic field,velocity,temperature and the degenerate density near the free boundary.We overcome the obstacle by establishing the lower bound of the temperature by using different Lagrangian coordinates,and deriving the uniform-in-time upper and lower bounds of the Lagrangian deformation variable r;by weighted estimates,and also the uniform-in-time weighted estimates of the higher-order derivatives of solutions by delicate analysis. 展开更多
关键词 compressible magnetohydrodynamic equations vacuum free boundary global axisymmetric classical solutions large initial data
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