A Priori Estimates for a System Modelling Nonhomogeneous Asymmetric Fluids

References

• Aero, E. L., Bulygin, A. N., Kuvshinskii, E. V. (1965). Asymmetric hydromechanics. J. Appl. Math. Mech. 29(2):333–346. DOI: 10.1016/0021-8928(65)90035-3.
   Google Scholar
• Boldrini, J. L., Rojas-Medar, M. (1996). On the convergence rate of spectral approximation for the equations for nonhomogeneous asymmetric fluids. ESAIM: M2AN. 30(2):123–155. DOI: 10.1051/m2an/1996300201231.
   Web of Science ®Google Scholar
• Boldrini, J. L., Rojas-Medar, M. A., Fernández-Cara, E. (2003). Semi-Galerkin approximation and strong solutions to the equations of the nonhomogeneous asymmetric fluids. J. Math. Pures Appl. (9). 82(11):1499–1525. DOI: 10.1016/j.matpur.2003.09.005.
   Web of Science ®Google Scholar
• Braz e Silva, P., Cruz, F. W., Rojas-Medar, M. (2014). Vanishing viscosity for non-homogeneous asymmetric fluids in R3: the L2 case. J. Math. Anal. Appl. 420(1):207–221.
   Web of Science ®Google Scholar
• Braz e Silva, P., Fernández-Cara, E., Rojas-Medar, M. A. (2007). Vanishing viscosity for non-homogeneous asymmetric fluids in R3. J. Math. Anal. Appl. 332(2):833–845.
   Web of Science ®Google Scholar
• Conca, C., Gormaz, R., Ortega-Torres, E. E., Rojas-Medar, M. A. (2002). The equations of non-homogeneous asymmetric fluids: an iterative approach. Math. Meth. Appl. Sci. 25(15):1251–1280. DOI: 10.1002/mma.331.
   Web of Science ®Google Scholar
• Łukaszewicz, G. (1990). On nonstationary flows of incompressible asymmetric fluids. Math. Meth. Appl. Sci. 13(3):219–232. DOI: 10.1002/mma.1670130304.
   Web of Science ®Google Scholar
• Łukaszewicz, G., Waluś, W., Piskorek, A. (1989). On stationary flows of asymmetric fluids with heat convection. Math. Meth. Appl. Sci. 11(3):343–351. DOI: 10.1002/mma.1670110304.
   Web of Science ®Google Scholar
• Rojas-Medar, M. A., Ortega-Torres, E. E. (2005). The equations of a viscous asymmetric fluid: an interactive approach. Z. Angew. Math. Mech. 85(7):471–489. DOI: 10.1002/zamm.199910189.
   Web of Science ®Google Scholar
• Vitoriano e Silva, F. (2013). On the steady viscous flow of a nonhomogeneous asymmetric fluid. Ann. Mat. 192(4):665–672. DOI: 10.1007/s10231-011-0242-x.
   Web of Science ®Google Scholar
• Łukaszewicz, G. (1999). Micropolar Fluids: Theory and Applications. Basel: Birkhauser.
   Google Scholar
• Fan, J., Nakamura, G. (2008). Local solvability of an inverse problem to the density-dependent Navier-Stokes equations. Appl. Anal. 87(10–11):1255–1265. DOI: 10.1080/00036810802428920.
   Web of Science ®Google Scholar
• Choulli, M., Imanuvilov, O. Y., Puel, J.-P., Yamamoto, M. (2013). Inverse source problem for linearized Navier-Stokes equations with data in arbitrary sub-domain. Appl. Anal. 92(10):2127–2143. DOI: 10.1080/00036811.2012.718334.
   Web of Science ®Google Scholar
• Imanuvilov, O. Y., Yamamoto, M. (1998). Lipschitz stability in inverse parabolic problems by the Carleman estimate. Inverse Prob. 14(5):1229–1245. DOI: 10.1088/0266-5611/14/5/009.
   Web of Science ®Google Scholar
• Lions, P. L. (1996). Mathematical Topics in Fluid Mechanics, Incompressible Models, Vol. 1. Oxford: Claredon Press, Oxford Science Publications.
   Google Scholar
• Lions, P. L. (1998). Mathematical Topics in Fluid Mechanics, Compressible Models, Vol. 2. Oxford: Claredon Press, Oxford Science Publications.
   Google Scholar
• Temam, R. (1977). Navier-Stokes Equations. Theory and Numerical Analysis. Studies in Mathematics and its Applications, vol. 2. Amsterdam: North-Holland Publishing Co.
   Google Scholar
• Boyer, F., Fabrie, P. (2013). Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models. Applied Mathematical Sciences, 183. New York: Springer.
   Google Scholar
• Heywood, J. G. (1980). The Navier-Stokes equations: on the existence, regularity and decay of solutions. Indiana Univ. Math. J. 29(5):639–681. DOI: 10.1512/iumj.1980.29.29048.
   Web of Science ®Google Scholar
• Evans, L. C. (2010). Partial Differential Equations, 2nd ed., Graduate Studies in Mathematics, 19. Providence, RI: American Mathematical Society.
   Google Scholar