Well-posedness for fractional Navier-Stokes equations in critical spaces close to (B) over dot(infinity,infinity)(-(2 beta-1))(R-n)

作者：Zhai Zhichun^*

来源：Dynamics of Partial Differential Equations, 2010, 7(1): 25-44.

• Navier-Stokes equations
• Magnetohydrodynamics equations
• BMO-zeta(Rn)
• Besov spaces

In this paper, we study the well-posedness for the fractional Navier-Stokes equations in critical spaces G(n)(-(2 beta-1))(R-n) and BMO-(2 beta-)(R-n) which are close to the largest critical space (B) over dot(infinity,infinity)(-(2 beta-1))(R-n). In G(n)(-(2 beta-1))(R-n), we establish the well-posedness based on a priori estimates for the fractional Navier-Stokes equations in Besov spaces. To obtain the well-posedness in BMO-(2 beta-)(R-n), we find a relationship between Q(alpha,infinity)(beta,-1)(R-n) and BMO(R-n) by giving an equivalent characterization of BMO-zeta(R-n). As an application, we get the well-posedness for fractional magnetohydrodynamics equations in G(n)(-(2 beta-1))(R-n) and BMO-(2 beta-)(R-n).

• 出版日期2010-3