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Well-posedness for the Navier-Stokes equations with datum in the Sobolev spaces

Autor: Khai, D. Q.

In this paper, we study local well-posedness for the Navier-Stokes \linebreak equations with arbitrary initial data in homogeneous Sobolev spaces $\dot{H}^s_p(\mathbb{R}^d)$ for $d \geq 2, p > \frac{d}{2},\ {\rm and}\ \frac{d}{p} - 1 \leq s < \frac{d

Externí odkaz: http://arxiv.org/abs/1608.06397

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On the initial value problem for the Navier-Stokes equations with the initial datum in the Sobolev spaces

Autor: Khai, D. Q., Duong, V. T. T.

In this paper, we study local well-posedness for the Navier-Stokes equations with arbitrary initial data in homogeneous Sobolev spaces $\dot{H}^s_p(\mathbb{R}^d)$ for $d \geq 2, p > \frac{d}{2},\ {\rm and}\ \frac{d}{p} - 1 \leq s < \frac{d}{2p}$. The

Externí odkaz: http://arxiv.org/abs/1603.04219

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The existence and decay rates of strong solutions for Navier-Stokes Equations in Bessel-potential spaces

Autor: Khai, D. Q.

In this paper, we prove some results on the existence and decay properties of high order derivatives in time and space variables for local and global solutions of the Cauchy problem for the Navier-Stokes equations in Bessel-potential spaces.
Com

Externí odkaz: http://arxiv.org/abs/1603.01896

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Well-posedness for the Navier-Stokes equations with data in homogeneous Sobolev-Lorentz spaces

Autor: Khai, D. Q., Tri, N. M.

Publikováno v: Nonlinear Analysis 2017

In this paper, we study local well-posedness for the Navier-Stokes equations (NSE) with the arbitrary initial value in homogeneous Sobolev-Lorentz spaces $\dot{H}^s_{L^{q, r}}(\mathbb{R}^d):= (-\Delta)^{-s/2}L^{q,r}$ for $d \geq 2, q > 1, s \geq 0$,

Externí odkaz: http://arxiv.org/abs/1601.01742

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On the initial value problem for the Navier-Stokes equations with the initial datum in critical Sobolev and Besov spaces

Autor: Khai, D. Q., Tri, N. M.

Publikováno v: J. Math. Sci. Univ. Tokyo 23 (2) (2016), 499-528

The existence of local unique mild solutions to the Navier-Stokes equations in the whole space with an initial tempered distribution datum in critical homogeneous or inhomogeneous Sobolev spaces is shown. Especially, the case when the integral-expone

Externí odkaz: http://arxiv.org/abs/1601.01726

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The existence and space-time decay rates of strong solutions to Navier-Stokes Equations in weighed $L^\infty(|x|^\gamma{\rm dx})\cap L^\infty(|x|^\beta{\rm dx})$ spaces

Autor: Khai, D. Q., Tri, N. M.

In this paper, we prove some results on theexistence and space-time decay rates of global strong solutions of the Cauchy problem for the Navier-Stokes equations in weighed $L^\infty(\mathbb R^d,|x|^\gamma{\rm dx})\cap L^\infty(\mathbb R^d,|x|^\beta{\

Externí odkaz: http://arxiv.org/abs/1601.01723

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Well-posedness for the Navier-Stokes equations with datum in Sobolev-Fourier-Lorentz spaces

Autor: Khai, D. Q., Tri, N. M.

Publikováno v: J. Math. Anal. Appl. 437 (2) (2016), 754-781

In this note, for $s \in \mathbb R$ and $1 \leq p, r \leq \infty$, we introduce and study Sobolev-Fourier-Lorentz spaces $\dot{H}^s_{\mathcal{L}^{p, r}}(\mathbb{R}^d)$. In the family spaces $\dot{H}^s_{\mathcal{L}^{p, r}}(\mathbb{R}^d)$, the critical

Externí odkaz: http://arxiv.org/abs/1601.01441

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