Navier–Stokes equations and nonlinear heat equations in modulation spaces with negative derivative indices

By T. Iwabuchi. 2010

69 citations recorded by the source corpus.

Abstract The Cauchy problems for Navier–Stokes equations and nonlinear heat equations are studied in modulation spaces M q , σ s ( R n ) . 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 M q , σ s ( R n ) for the existence of local and global solutions for initial data u 0 ∈ M q , σ s ( R n ) .

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1304e767a8ab12e5e0431de98581bb282bd8dd88

Citations in the corpus

• The Navier-Stokes equations and weak Herz spaces (2011, unknown): “There are many papers which studied Navier-Stokes equations on several function spaces, for example, [2], [17], [9], [13], [14], [21], [23], [24], [27], [30], [33], [32], [38], [40], [44], [45] etc.”