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Navier-Stokes Equations in Complex Space

Nikolai Nadirashvili

Abstract

We prove global in time regularity of solutions of the Navier-Stokes equations defined in the complex space.

Navier-Stokes Equations in Complex Space

Abstract

We prove global in time regularity of solutions of the Navier-Stokes equations defined in the complex space.
Paper Structure (6 sections, 25 theorems, 327 equations)

This paper contains 6 sections, 25 theorems, 327 equations.

Table of Contents

  1. Introduction
  2. Complex Navier-Stokes equations
  3. Functional spaces. Hypoelliptic operators
  4. Holomorphic solenoidal vector fields
  5. Proof of Theorem \ref{['NN']}
  6. Discusion

Key Result

Theorem 1.1

Let $w^0\in L^2(M), \; \hbox{div} \, w^0 = 0$, $f\in L^2(\Omega \times (0,T) )$ and for any $T>0, \, \hbox{div} \, f = 0$ in the sense of distributions. Then there exists at least one Leray-Hopf weak solution of the problem NS, div, CP in $M\times [0, \infty )$.

Theorems & Definitions (25)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 2.1
  • Theorem 2.2
  • Proposition 2.3
  • Theorem 2.4
  • Theorem 2.5
  • Theorem 3.1
  • Theorem 3.2
  • Proposition 3.3
  • ...and 15 more