We prove an optimal extension and trace theorem for Sobolev spaces of nonlocal operators.
The extension is given by a suitable Poisson integral and solves the corresponding nonlocal …

We consider fractional Navier-Stokes equations in a smooth bounded domain Ω⊂ RN, N≥
2. Following the geometric theory of abstract parabolic problems we give the detailed …

Abstract We consider the Navier–Stokes equation (NS) in dimensions two and three as limits
of the fractional approximations. In 2-D the NS problem is critical with respect to the standard …

In this paper, we consider the dynamics for damped generalized incompressible Navier–
Stokes equations defined on ℝ 2. The generalized Navier–Stokes equations here refer to …

Our purpose is to formulate an abstract result, motivated by the recent paper [8], allowing to
treat the solutions of critical and super-critical equations as limits of solutions to their …

The 2D Quasi-geostrophic equation attracts attention of mathematicians through recent
years; see for example [2, 7, 8, 10, 12, 13, 16, 17, 20, 21, 39]. While the sub-critical problems …

Our task here is to use a version of the 'vanishing viscosity technique'to study the critical 2D
Quasi-Geostrophic equation. The present paper extends and specializes the results …

On the Cauchy problem for hyperdissipative Navier–Stokes equations in super-critical Besov
and Triebel–Lizorkin spaces - ScienceDirect Skip to main contentSkip to article Elsevier logo …

Solvability of Dirichlet's problem for the subcritical fractional Burgers equation is discussed
here in two base spaces: $ L^ 2 (I) $ and $ H^ s (I) $ with $ s\gt {1/2} $. A solution in the …

Finite dimensionality of the global attractor for a fractional Schrödinger equation on R - ScienceDirect
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