Carleman estimate for the Navier–Stokes equations and an application to a lateral Cauchy problem

Inverse Problems ◽

10.1088/0266-5611/32/2/025001 ◽

2016 ◽

Vol 32 (2) ◽

pp. 025001 ◽

Author(s):

Mourad Bellassoued ◽

Oleg Imanuvilov ◽

Masahiro Yamamoto

Keyword(s):

Cauchy Problem ◽

Stokes Equations ◽

Carleman Estimate ◽

Navier Stokes ◽

Navier Stokes Equations

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On global weak solutions to the Cauchy problem for the Navier–Stokes equations with largeL3-initial data

Nonlinear Analysis ◽

10.1016/j.na.2016.01.018 ◽

2017 ◽

Vol 154 ◽

pp. 269-296 ◽

Author(s):

G. Seregin ◽

V. Šverák

Keyword(s):

Cauchy Problem ◽

Initial Data ◽

Weak Solutions ◽

Stokes Equations ◽

Navier Stokes ◽

Global Weak Solutions ◽

Navier Stokes Equations ◽

The Cauchy Problem

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Non-existence of Classical Solutions with Finite Energy to the Cauchy Problem of the Compressible Navier–Stokes Equations

Archive for Rational Mechanics and Analysis ◽

10.1007/s00205-018-1328-z ◽

2018 ◽

Vol 232 (2) ◽

pp. 557-590 ◽

Author(s):

Hai-Liang Li ◽

Yuexun Wang ◽

Zhouping Xin

Keyword(s):

Cauchy Problem ◽

Stokes Equations ◽

Finite Energy ◽

Navier Stokes ◽

Classical Solutions ◽

Navier Stokes Equations ◽

The Cauchy Problem

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Global existence and large time asymptotic behavior of strong solutions to the Cauchy problem of 2D density-dependent Navier–Stokes equations with vacuum

Nonlinearity ◽

10.1088/1361-6544/aab31f ◽

2018 ◽

Vol 31 (6) ◽

pp. 2617-2632 ◽

Author(s):

Boqiang Lü ◽

Xiaoding Shi ◽

Xin Zhong

Keyword(s):

Cauchy Problem ◽

Asymptotic Behavior ◽

Global Existence ◽

Stokes Equations ◽

Strong Solutions ◽

Navier Stokes ◽

Navier Stokes Equations ◽

The Cauchy Problem ◽

Time Asymptotic Behavior

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Exact solutions for the Cauchy problem to the 3D spherically symmetric incompressible Navier-Stokes equations

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30783-5 ◽

2018 ◽

Vol 38 (3) ◽

pp. 778-790

Author(s):

Jianlin ZHANG ◽

Yuming QIN

Keyword(s):

Cauchy Problem ◽

Exact Solutions ◽

Stokes Equations ◽

Navier Stokes ◽

Spherically Symmetric ◽

Navier Stokes Equations ◽

The Cauchy Problem

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Global classical solution to the cauchy problem of the 3-D compressible Navier-Stokes equations with density-dependent viscosity

Acta Mathematica Scientia ◽

10.1016/s0252-9602(16)30078-9 ◽

2016 ◽

Vol 36 (5) ◽

pp. 1419-1432 ◽

Author(s):

Yulin YE

Keyword(s):

Cauchy Problem ◽

Classical Solution ◽

Stokes Equations ◽

Navier Stokes ◽

Global Classical Solution ◽

Navier Stokes Equations ◽

Density Dependent ◽

The Cauchy Problem ◽

Dependent Viscosity

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Cauchy problem of semi-linear parabolic equations with weak data in homogeneous space and application to the Navier-Stokes equations

Science in China Series A Mathematics ◽

10.1360/02ys0097 ◽

2003 ◽

Vol 46 (5) ◽

pp. 641

Author(s):

Changxing MIAO

Keyword(s):

Cauchy Problem ◽

Homogeneous Space ◽

Parabolic Equations ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Linear Parabolic Equations

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Existence of global strong solution to Cauchy problem for one-dimensional barotropic compressible Navier–Stokes equations

Applicable Analysis ◽

10.1080/00036811.2014.987133 ◽

2014 ◽

Vol 94 (12) ◽

pp. 2418-2434

Author(s):

Ruxu Lian ◽

Jian Liu

Keyword(s):

Cauchy Problem ◽

Strong Solution ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations ◽

One Dimensional ◽

Global Strong Solution

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Global well-posedness of the Cauchy problem for the Navier-Stokes equations of nonisentropic flow with discontinuous initial data

Journal of Differential Equations ◽

10.1016/0022-0396(92)90042-l ◽

1992 ◽

Vol 95 (1) ◽

pp. 33-74 ◽

Author(s):

David Hoff

Keyword(s):

Cauchy Problem ◽

Initial Data ◽

Stokes Equations ◽

Navier Stokes ◽

Well Posedness ◽

Navier Stokes Equations ◽

Discontinuous Initial Data ◽

The Cauchy Problem

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Global Well-Posedness to the 3D Cauchy Problem of Nonhomogeneous Heat Conducting Navier–Stokes Equations with Vacuum and Large Oscillations

Journal of Mathematical Fluid Mechanics ◽

10.1007/s00021-021-00649-0 ◽

2021 ◽

Vol 24 (1) ◽

Author(s):

Xin Zhong

Keyword(s):

Cauchy Problem ◽

Stokes Equations ◽

Navier Stokes ◽

Heat Conducting ◽

Well Posedness ◽

Navier Stokes Equations ◽

Nonhomogeneous Heat

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Existence of strong solution for the Cauchy problem of fully compressible Navier-Stokes equations in two dimensions

Discrete & Continuous Dynamical Systems - B ◽

10.3934/dcdsb.2020348 ◽

2017 ◽

Vol 22 (11) ◽

pp. 0-0

Author(s):

Zhilei Liang ◽

◽

Jiangyu Shuai

Keyword(s):

Cauchy Problem ◽

Strong Solution ◽

Stokes Equations ◽

Two Dimensions ◽

Navier Stokes ◽

Navier Stokes Equations ◽

The Cauchy Problem

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