Global solutions of Navier-Stokes equations for large initial data belonging to spaces with dominating mixed smoothness

Abstract Navier–Stokes equations have unique solutions, global in time, for large initial data belonging to spaces with dominating mixed smoothness if they are small at finitely many distinguished sampling points and decay moderately.

[1]  H. Triebel.  Theory of Function Spaces III , 2008 .

[2]  Jan Vybíral,et al.  Sampling numbers and function spaces , 2007, J. Complex..

[3]  Winfried Sickel,et al.  Spaces of functions of mixed smoothness and approximation from hyperbolic crosses , 2004, J. Approx. Theory.

[4]  Hans Triebel.  Faber Systems and Their Use in Sampling, Discrepancy, Numerical Integration , 2012 .

[5]  H. Schmeißer.  Recent developments in the theory of function spaces with dominating mixed smoothness , 2007 .

[6]  R. Danchin,et al.  Fourier Analysis and Nonlinear Partial Differential Equations , 2011 .

[7]  E. Novak,et al.  Tractability of Multivariate Problems , 2008 .

[8]  H. Triebel.  Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration , 2010 .

[9]  H. Triebel.  Spaces of Besov-Hardy-Sobolev type , 1978 .

[10]  General Function Spaces, V. (The Spaces B g(x)p, q and F g(x)p, q: The Case 0 , 1979 .

[11]  Jan Vybíral.  Function spaces with dominating mixed smoothness , 2006 .

[12]  Lena Schwartz,et al.  Theory Of Function Spaces Ii , 2016 .

[13]  H. Triebel.  Theory Of Function Spaces , 1983 .

[14]  H. Triebel.  Hybrid Function Spaces, Heat and Navier-stokes Equations , 2015 .

[15]  Herbert Koch,et al.  Well-posedness for the Navier–Stokes Equations , 2001 .

[16]  H. Triebel,et al.  Topics in Fourier Analysis and Function Spaces , 1987 .

[17]  H. Triebel.  Local Function Spaces, Heat and Navier-stokes Equations , 2013 .

[18]  Pierre Gilles Lemarié-Rieusset,et al.  Recent Developments in the Navier-Stokes Problem , 2002 .

[19]  Marco Cannone,et al.  Chapter 3 - Harmonic Analysis Tools for Solving the Incompressible Navier–Stokes Equations , 2005 .