• Václav Mácha
  • (Institute of Mathematics, CAS)
  • Global BMO estimates for non-Newtonian fluids with perfect slip boundary conditions
  • Abstract:
  • We study the generalized stationary Stokes system in a bounded domain in the plane equipped with perfect slip boundary conditions. We show natural stability results in oscillatory spaces, i.e. Hölder spaces and Campanato spaces including the border line spaces of bounded mean oscillations (BMO) and vanishing mean oscillations (VMO). Especially we show that under appropriate assumptions gradients of solutions are globally continues. Since the stress tensor is assumed to be governed by a general Orlicz function, our theory includes various cases of (possibly degenerate) shear thickening and shear thinning fluids; including the model case of power law fluids. It is a joint work with Sebastian Schwarzacher.
  • 24.10.17   09:00

  • Ji?í Neustupa
  • (Institute of Mathematics, CAS)
  • A contribution to the theory of regularity of a weak solution to the Navier-Stokes equations via one component of velocity and other related quantities
  • Abstract:
  • We deal with a suitable weak solution (v,p) to the Navier-Stokes equations, where v=(v_1,v_2,v_3). We give a brief survey of known criteria of regularity that use assumptions on just one component of v. We show that the regularity of (v,p) at a space-time point (x_0,t_0) is essentially determined by the Serrin-type integrability of the positive part of a certain linear combination of v_1^2, v_2^2, v_3^2 and p in a backward neighborhood of (x_0,t_0). An appropriate choice of coefficients in the linear combination leads to the Serrin-type condition on one component of v or, alternatively, on the positive part of the Bernoulli pressure (1/2)|v|^2+p or the negative part of p, etc.
  • 17.10.17   09:00

prof. RNDr. Eduard Feireisl, DrSc.
Šárka Nečasová, Milan Pokorný