was presented by professor Mu­kh­tar­bay Otel­ba­ev, director of the Eurasian Mathematical Institute of the Eurasian National University in Astana, Kazachstan (Институт математики и математического моделирования, Евразийский национальный университет, Aстана).
News was sent on  January ^10th 2014 (10:33 GMT)  Agency  www.BNews.kz (Главные новости Казахстана).

The decision approving the results and granting of award will be taken following the procedure
at the earliest 2 years after the publication (See the rules at the end)

Original paper is available at:
http://www.math.kz/images/journal/2013-4/2013-4.rar  ←

Математический журнал 2013. Том 13,№4(50),5-104     EISSN 1682 0525
УДК .517.9
Мухтарбай Отелбаев
Институт математики и математического моделирования МОИ РК
050010, Алматы, ул. Пушкина, 125, e-mail: otelbaevm@mail.ru

СУЩЕСТВОВАНИЕ  СИЛЬНОГО  РЕШЕНИЯ УРАВНЕНИЯ  НАВЬЕ-СТОКСА

R работе дано решение шестой проблемы тысячелетия (The Millennium Prize Problems): доказаны существование к единственность сильного решения трехмерной задачи Навье-Стокса с периодическими краевыми условиями по пространственным переменным.
Ключевые слова: шестая проблема тысячелетия, уравнение Навье-
Стокса, сильное решение.
© Мухтарбай Отелбаев, 2013.
Статья поступила в редакцию 23.01.12
Окончательный вариант 20.12.13

A fragment of English translation:
Mukhtarbay Otelbaev
THE EXISTENCE OF A STRONG SOLUTION TO THE NAVIER-STOKES EQUATIONS

Institute of Mathematics and Mathematical Modeling MES RK
125 Pushkin St, Almaty 050010, email: otelbaevm@mail.ru
ISSN 1682-0525. Mathematical Journal. 2013. Vol 13, Num 4 (50).
Translated by Mikhail Wolfson, Ph.D., January 12, 2014

Abstract
In this work, a solution to the sixth Millennium Prize Problem is provided: the existence and uniqueness of a strong solution
to the three-dimensional Navier-Stokes problem with periodic spatial boundary conditions.
Keywords: sixth Millennium Prize problem, Navier-Stokes equation, strong solution.

Full text of the paper (and part of translation) is available at:
GitHub – World's largest open source community:
https://github.com/myw/navier_stokes_translate/archive/master.zip

Professor Mukhtarbay Otelbaev is the winner of the title “Man of Science of the Year" in contest "Altyn Adam" ("Man of the Year in Kazakhstan " in the category "Science") 2002; in 2002-2003, 2004 – 2005 is the Winner of the state scientific grant for scientists and experts who have made outstanding contributions to the development of science and technology, winner of the Economic Cooperation Organization in the "Science and Technology“, 2004, winner of the MES grant of the RK "Best university teacher", laureate of the State Prize of the Republic Kazakhstan in the field of science and technology.
(in English) http://otelbaev.com/?p=1
(in English) http://www.enu.kz/en/info/news/24736/?sphrase_id=150607
(in Russian) http://www.enu.kz/ru/lica-enu/otelbaev-mukhtarbay/

Scientific publications by Mukhtarbay Otelbaev
at Google Scholar ←
at ZentralBlatt  ←

Millennium Prize Problems

The Clay Mathematics Institute (CMI) is a privately funded operating foundation dedicated to increasing and disseminating mathematical knowledge. The CMI supports the work of leading researchers at various stages of their careers and organizes conferences, workshops, and an annual summer school. Contemporary breakthroughs are recognized by its annual Research Award.
In order to celebrate mathematics in the new millennium, the Clay Mathematics Institute of Cambridge, Massachusetts (CMI) established seven Prize Problems:

• Yang–Mills and Mass Gap
• Riemann Hypothesis
• P vs NP Problem
• Hodge Conjecture
• Poincaré Conjecture
• Navier–Stokes Equation
  [http://www.claymath.org/sites/default/files/navierstokes.pdf]
• Birch and Swinnerton-Dyer Conjecture

Following the decision of the Scientific Advisory Board, the Board of Directors of CMI designated a $7 million prize fund for the solutions
to these problems, with $1 million allocated to the solution of each problem

Rules for the Millennium Prizes (abridgement)

• A proposed solution to one of the Millennium Prize Problems may not be submitted directly to the Clay Mathematics Institute (CMI)
  for consideration.
• Before consideration, a proposed solution must be published in a refereed mathematics publication of worldwide reputation.
• It must also have general acceptance in the mathematics community 2 years after. Following this two-year waiting period
  the Scientific Advisory Board of CMI (SAB) will decide whether a solution merits detailed consideration.
• In the affirmative case, the SAB will constitute a special advisory committee will report within a reasonable time to the SAB.
  Based on this report and possible further investigation, the SAB will make a recommendation to the Directors.
• If the SAB cannot come to a clear decision about the correctness of a solution to a problem, its attribution, or the appropriateness
  of an award, the SAB may recommend that no prize be awarded for a particular problem.
• All decision-making procedures concerning the CMI Millennium Prize Problems are private. No records of these deliberations
  or related correspondence may be made public unless 50 years time have elapsed after the event in question