Y spaces and global smooth solution of fractional Navier–Stokes equations with initial value in the critical oscillation spaces
Copyright policy )Y spaces and global smooth solution of fractional Navier–Stokes equations with initial value in the critical oscillation spaces
The Cauchy problem to the fractional Navier-Stokes equations is studied in the paper. \[ \frac{\partial u}{\partial t}+(u\cdot\nabla)u+(-\Delta)^\beta u-\nabla p=0,\quad \text{div}\,u=0, \quad x\in\mathbb{R}^n,\;t>0, \] \[ u(x,0)=u_0(x),\;x\in\mathbb{R}^n. \] Here \(n\geq 2\), \(1/2<\beta<1\), \((-\Delta)^\beta\) is the \(\beta\)-order Laplace operator. The problem is investigated in a wide class of spaces including Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces. It is proved that if the initial data \(u_0\) has a small norm then the problem has a unique smooth global solution. The spaces used are described in detail in the article. It should be noted that not all designations are defined, and this makes it difficult to read the work.
- Wuhan University China (People's Republic of)
- Wuhan Textile University China (People's Republic of)
parameter Meyer wavelets, fractional Navier-Stokes equations, Besov-Morrey spaces, global solvability, Navier-Stokes equations, Existence, uniqueness, and regularity theory for incompressible viscous fluids, Fractional partial differential equations, Triebel-Lizorkin-Morrey spaces, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
parameter Meyer wavelets, fractional Navier-Stokes equations, Besov-Morrey spaces, global solvability, Navier-Stokes equations, Existence, uniqueness, and regularity theory for incompressible viscous fluids, Fractional partial differential equations, Triebel-Lizorkin-Morrey spaces, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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