چکیده (انگلیسی):

The Cauchy problems for Navier–Stokes equations and nonlinear heat equations are studied in modulation spaces Msq,σ (Rn). Though the case of the derivative index s = 0 has been treated in our previous work, the case s ≠ 0 is also treated in this paper. Our aim is to reveal the conditions of s, q and σ of Msq,σ (Rn) for the existence of local and global solutions for initial data u0 ∈ Msq,σ (Rn).