The Experts below are selected from a list of 3558 Experts worldwide ranked by ideXlab platform
Takahito Kashiwabara - One of the best experts on this subject based on the ideXlab platform.
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the hydrostatic stokes semigroup and well posedness of the primitive equations on spaces of bounded functions
Journal of Functional Analysis, 2020Co-Authors: Yoshikazu Giga, Mathis Gries, Matthias Hieber, Amru Hussein, Takahito KashiwabaraAbstract:Abstract Consider the 3-d primitive equations in a layer domain Ω = G × ( − h , 0 ) , G = ( 0 , 1 ) 2 , subject to mixed Dirichlet and Neumann Boundary Conditions at z = − h and z = 0 , respectively, and the periodic Lateral Boundary Condition. It is shown that this equation is globally, strongly well-posed for arbitrary large data of the form a = a 1 + a 2 , where a 1 ∈ C ( G ‾ ; L p ( − h , 0 ) ) , a 2 ∈ L ∞ ( G ; L p ( − h , 0 ) ) for p > 3 , and where a 1 is periodic in the horizontal variables and a 2 is sufficiently small. In particular, no differentiability Condition on the data is assumed. The approach relies on L H ∞ L z p ( Ω ) -estimates for terms of the form t 1 / 2 ‖ ∂ z e t A σ ‾ P f ‖ L H ∞ L z p ( Ω ) ≤ C e t β ‖ f ‖ L H ∞ L z p ( Ω ) for t > 0 , where e t A σ ‾ denotes the hydrostatic Stokes semigroup. The difficulty in proving estimates of this form is that the hydrostatic Helmholtz projection P fails to be bounded with respect to the L ∞ -norm. The global strong well-posedness result is then obtained by an iteration scheme, splitting the data into a smooth and a rough part and by combining a reference solution for smooth data with an evolution equation for the rough part.
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the hydrostatic stokes semigroup and well posedness of the primitive equations on spaces of bounded functions
arXiv: Analysis of PDEs, 2018Co-Authors: Yoshikazu Giga, Mathis Gries, Matthias Hieber, Amru Hussein, Takahito KashiwabaraAbstract:Consider the $3$-d primitive equations in a layer domain $\Omega=G \times (-h,0)$, $G=(0,1)^2$, subject to mixed Dirichlet and Neumann Boundary Conditions at $z=-h$ and $z=0$, respectively, and the periodic Lateral Boundary Condition. It is shown that this equation is globally, strongly well-posed for arbitrary large data of the form $a=a_1 + a_2$, where $a_1\in C(\overline{G};L^p(-h,0))$, $a_2\in L^{\infty}(G;L^p(-h,0))$ for $p>3$, and where $a_1$ is periodic in the horizontal variables and $a_2$ is sufficiently small. In particular, no differentiability Condition on the data is assumed. The approach relies on $L^\infty_HL^p_z(\Omega)$-estimates for terms of the form $t^{1/2} \lVert \partial_z e^{tA_{\overline{\sigma}}}\mathbb{P}f \rVert_{L^\infty_H L^p_z(\Omega)}\le C e^{t\beta} \lVert f \rVert_{L^\infty_H L^p_z (\Omega)}$ for $t>0$, where $e^{t A_{\overline{\sigma}}}$ denotes the hydrostatic Stokes semigroup. The difficulty in proving estimates of this form is that the hydrostatic Helmholtz projection $\mathbb{P}$ fails to be bounded with respect to the $L^\infty$-norm. The global strong well-posedness result is then obtained by an iteration scheme, splitting the data into a smooth and a rough part and by combining a reference solution for smooth data with an evolution equation for the rough part.
David H Bromwich - One of the best experts on this subject based on the ideXlab platform.
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a harmonic fourier spectral limited area model with an external wind Lateral Boundary Condition
Monthly Weather Review, 1997Co-Authors: Qiu-shi Chen, Lesheng Bai, David H BromwichAbstract:In comparison to the Tatsumi’s spectral method, the harmonic-Fourier spectral method has two major advantages. 1) The semi-implicit scheme is quite efficient because the solutions of the Poisson and Helmholtz equations are readily derived. 2) The Lateral Boundary value problem of a limited-area model is easily solved. These advantages are the same as those of the spherical harmonics used in global models if the singularity at the pole points for a globe is considered to be the counterpart of the Lateral Boundary Condition for a limited region. If a limited-area model is nested in a global model, the prediction of the limited-area model at each time step is the sum of the inner part and the harmonic part predictions. The inner part prediction is solved by the double sine series from the inner part equations for the limited-area model. The harmonic part prediction is derived from the prediction of the global model. An external wind Lateral Boundary method is proposed based on the basic property of the wind separation in a limited region. The Boundary values of a limited-area model in this method are not given at the closed Boundary line, but always given by harmonic functions defined throughout the limited domain. The harmonic functions added to the inner parts at each time step represent the effects of the Lateral Boundary values on the prediction of the limited-area model, and they do not cause any discontinuity near the Boundary. Tests show that predicted motion systems move smoothly in and out through the Boundary, where the predicted variables are very smooth without any other Boundary treatment. In addition, the Boundary method can also be used in the most complicated mountainous region where the Boundary intersects high mountains. The tests also show that the adiabatic dynamical part of the limited-area model very accurately predicts the rapid development of a cyclone caused by dry baroclinic instability along the east coast of North America and a lee cyclogenesis case in East Asia. The predicted changes of intensity and location of both cyclones are close to those given by the observations.
Judith Berner - One of the best experts on this subject based on the ideXlab platform.
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predictability of tropical cyclone intensity scale dependent forecast error growth in high resolution stochastic kinetic energy backscatter ensembles
Quarterly Journal of the Royal Meteorological Society, 2016Co-Authors: Falko Judt, Shuyi S Chen, Judith BernerAbstract:A systematic study of the intrinsic predictability of tropical cyclone (TC) intensity is conducted using a set of cloud-resolving model ensembles of Hurricane Earl (2010). The ensembles are perturbed with a stochastic kinetic-energy backscatter scheme (SKEBS) and started from identical initial Conditions. Scale-dependent error growth is investigated by imposing stochastic perturbations with various spatial scales on the TC and its environment. Predictability limits (upper bound) are determined by computing the error magnitude associated with each component of the Fourier-decomposed TC wind fields at forecast times up to 7 days. Three SKEBS ensembles with different perturbation scales are used to investigate the effects of small-scale, mesoscale and large-scale uncertainties on the predictability of TC intensity. In addition, the influence of the environmental flow is investigated by perturbing the Lateral Boundary Conditions. It is found that forecast errors grow rapidly on small scales (azimuthal wave numbers > 20), which saturate within 6–12 h in all four ensembles, regardless of perturbation scale. Errors grow relatively slower on scales corresponding to rain bands (wave numbers 2–5), limiting the predictability of these features to 1–5 days. Earl's mean vortex and the wave number-1 asymmetry are comparatively resistant to error growth and remain predictable for at least 7 days. Forecast uncertainty of the mean vortex and wave number-1 asymmetry is greater in the large-scale perturbation and perturbed Lateral Boundary Condition ensembles. The results from this case indicate that the predictability of the mean vortex and wave number-1 asymmetry is predominately associated with the predictability of the large-scale environment, which is generally much longer than that of convective-scale processes within the TC.
Yoshikazu Giga - One of the best experts on this subject based on the ideXlab platform.
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the hydrostatic stokes semigroup and well posedness of the primitive equations on spaces of bounded functions
Journal of Functional Analysis, 2020Co-Authors: Yoshikazu Giga, Mathis Gries, Matthias Hieber, Amru Hussein, Takahito KashiwabaraAbstract:Abstract Consider the 3-d primitive equations in a layer domain Ω = G × ( − h , 0 ) , G = ( 0 , 1 ) 2 , subject to mixed Dirichlet and Neumann Boundary Conditions at z = − h and z = 0 , respectively, and the periodic Lateral Boundary Condition. It is shown that this equation is globally, strongly well-posed for arbitrary large data of the form a = a 1 + a 2 , where a 1 ∈ C ( G ‾ ; L p ( − h , 0 ) ) , a 2 ∈ L ∞ ( G ; L p ( − h , 0 ) ) for p > 3 , and where a 1 is periodic in the horizontal variables and a 2 is sufficiently small. In particular, no differentiability Condition on the data is assumed. The approach relies on L H ∞ L z p ( Ω ) -estimates for terms of the form t 1 / 2 ‖ ∂ z e t A σ ‾ P f ‖ L H ∞ L z p ( Ω ) ≤ C e t β ‖ f ‖ L H ∞ L z p ( Ω ) for t > 0 , where e t A σ ‾ denotes the hydrostatic Stokes semigroup. The difficulty in proving estimates of this form is that the hydrostatic Helmholtz projection P fails to be bounded with respect to the L ∞ -norm. The global strong well-posedness result is then obtained by an iteration scheme, splitting the data into a smooth and a rough part and by combining a reference solution for smooth data with an evolution equation for the rough part.
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the hydrostatic stokes semigroup and well posedness of the primitive equations on spaces of bounded functions
arXiv: Analysis of PDEs, 2018Co-Authors: Yoshikazu Giga, Mathis Gries, Matthias Hieber, Amru Hussein, Takahito KashiwabaraAbstract:Consider the $3$-d primitive equations in a layer domain $\Omega=G \times (-h,0)$, $G=(0,1)^2$, subject to mixed Dirichlet and Neumann Boundary Conditions at $z=-h$ and $z=0$, respectively, and the periodic Lateral Boundary Condition. It is shown that this equation is globally, strongly well-posed for arbitrary large data of the form $a=a_1 + a_2$, where $a_1\in C(\overline{G};L^p(-h,0))$, $a_2\in L^{\infty}(G;L^p(-h,0))$ for $p>3$, and where $a_1$ is periodic in the horizontal variables and $a_2$ is sufficiently small. In particular, no differentiability Condition on the data is assumed. The approach relies on $L^\infty_HL^p_z(\Omega)$-estimates for terms of the form $t^{1/2} \lVert \partial_z e^{tA_{\overline{\sigma}}}\mathbb{P}f \rVert_{L^\infty_H L^p_z(\Omega)}\le C e^{t\beta} \lVert f \rVert_{L^\infty_H L^p_z (\Omega)}$ for $t>0$, where $e^{t A_{\overline{\sigma}}}$ denotes the hydrostatic Stokes semigroup. The difficulty in proving estimates of this form is that the hydrostatic Helmholtz projection $\mathbb{P}$ fails to be bounded with respect to the $L^\infty$-norm. The global strong well-posedness result is then obtained by an iteration scheme, splitting the data into a smooth and a rough part and by combining a reference solution for smooth data with an evolution equation for the rough part.
Tsingchang Chen - One of the best experts on this subject based on the ideXlab platform.
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contributions of mixed physics versus perturbed initial Lateral Boundary Conditions to ensemble based precipitation forecast skill
Monthly Weather Review, 2008Co-Authors: Adam J Clark, William A Gallus, Tsingchang ChenAbstract:Abstract An experiment is described that is designed to examine the contributions of model, initial Condition (IC), and Lateral Boundary Condition (LBC) errors to the spread and skill of precipitation forecasts from two regional eight-member 15-km grid-spacing Weather Research and Forecasting (WRF) ensembles covering a 1575 km × 1800 km domain. It is widely recognized that a skillful ensemble [i.e., an ensemble with a probability distribution function (PDF) that generates forecast probabilities with high resolution and reliability] should account for both error sources. Previous work suggests that model errors make a larger contribution than IC and LBC errors to forecast uncertainty in the short range before synoptic-scale error growth becomes nonlinear. However, in a regional model with unperturbed LBCs, the infiltration of the Lateral boundaries will negate increasing spread. To obtain a better understanding of the contributions to the forecast errors in precipitation and to examine the window of foreca...
