Global well-posedness for passively transported nonlinear moisture dynamics with phase changes

Hittmeir, Sabine; Klein, Rupert; Li, Jinkai; Titi, Edriss S.

doi:10.1088/1361-6544/aa82f1

Cited by 24 publications

(39 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, the coupling to moisture and its analysis has come into focus, see and the references given therein. The equation for the moisture q is of the type

\begin{matrix} true \\ right \partial_{t} q + v \cdot \nabla_{H} q + w \cdot \partial_{z} q - normalΔ q = h + F (v, τ, q) \end{matrix}

with additional coupling term

F (v, τ, q)

.…”

Section: Discussionmentioning

confidence: 99%

“…In the model studied in

F (v, τ, q)

involves some Heaviside functions and it is treated using variational methods. In water vapor

q_{v}

, cloud water

q_{c}

and rain water

q_{r}

mixing ratios are coupled to the temperature and velocity equations where the coupling terms involve expressions of the form

τ {(q_{r}^{+})}^{β} (q_{v s} - q_{v}), β \in false(0, 1 false], q_{r}^{+} = \max \{0, q_{r}\}

for fixed saturation mixing ratio

q_{v s}

. For

β = 1

this is Lipschitz continuous, and hence maximal

L^{q}

‐regularity can be used, while for

β < 1

other methods must be applied.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Analyticity of solutions to the primitive equations

Giga

Gries

Hieber

et al. 2019

Mathematische Nachrichten

View full text Add to dashboard Cite

This article presents the maximal regularity approach to the primitive equations. It is proved that the 3 primitive equations on cylindrical domains admit a unique global strong solution for initial data lying in the critical solonoidal Besov space 2∕ for , ∈ (1, ∞) with 1∕ + 1∕ ≤ 1. This solution regularize instantaneously and becomes even real analytic for > 0. K E Y W O R D S global strong well-posedness, maximal regularity, primitive equations, regularity of solutions M S C ( 2 0 1 0 ) Primary: 35Q35; Secondary: 76D03, 47D06, 86A05 284

show abstract

“…Recently, the coupling to moisture and its analysis has come into focus, see and the references given therein. The equation for the moisture q is of the type

\begin{matrix} true \\ right \partial_{t} q + v \cdot \nabla_{H} q + w \cdot \partial_{z} q - normalΔ q = h + F (v, τ, q) \end{matrix}

with additional coupling term

F (v, τ, q)

.…”

Section: Discussionmentioning

confidence: 99%

“…In the model studied in

F (v, τ, q)

involves some Heaviside functions and it is treated using variational methods. In water vapor

q_{v}

, cloud water

q_{c}

and rain water

q_{r}

mixing ratios are coupled to the temperature and velocity equations where the coupling terms involve expressions of the form

τ {(q_{r}^{+})}^{β} (q_{v s} - q_{v}), β \in false(0, 1 false], q_{r}^{+} = \max \{0, q_{r}\}

for fixed saturation mixing ratio

q_{v s}

. For

β = 1

this is Lipschitz continuous, and hence maximal

L^{q}

‐regularity can be used, while for

β < 1

other methods must be applied.…”

Section: Discussionmentioning

confidence: 99%

Analyticity of solutions to the primitive equations

Giga

Gries

Hieber

et al. 2019

Mathematische Nachrichten

View full text Add to dashboard Cite

show abstract

“…In [36], in a domain with small depth, the authors address the global existence of strong solutions to PE. The well-posedness of unique global strong solutions was obtained by Cao and Titi in [12] (see, also, [7][8][9][10][11]13,15,31,34] and the references therein for related studies). Considering the inviscid primitive equations, or hydrostatic incompressible Euler equations, the existence of solutions in the analytic function space and in the H s space are established in [5,40,53].…”

Section: The Compressible Primitive Equationsmentioning

confidence: 94%

Zero Mach Number Limit of the Compressible Primitive Equations: Well-Prepared Initial Data

Liu

Titi

2020

Arch Rational Mech Anal

View full text Add to dashboard Cite

This work concerns the zero Mach number limit of the compressible primitive equations. The primitive equations with the incompressibility condition are identified as the limiting equations. The convergence with well-prepared initial data (i.e., initial data without acoustic oscillations) is rigorously justified, and the convergence rate is shown to be of order O(ε), as ε → 0 + , where ε represents the Mach number. As a byproduct, we construct a class of global solutions to the compressible primitive equations, which are close to the incompressible flows.

show abstract

“…The multi-species model that we consider in this article is described below. Meanwhile, a different model for multi-species humid atmosphere was introduced in [KM06] and studied from the mathematical viewpoint in the recent article [HKLT17]. As explained in [KM06] (see after p9q in [KM06]), it is often assumed in cloud microphysics parameterizations that the vapor-to-cloud water conversion is instantaneous, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…See [Gra98] and other references below; this is our point of view here. In [KM06] and [HKLT17], the authors do not assume this limiting behavior from the outset and demonstrate how it may be derived in a consistent asymptotic framework given large but finite condensation rates. This is the main deviation of the bulk microphysics description in [KM06] from the scheme related to [Gra98] that we study here.…”

Section: Introductionmentioning

confidence: 99%

The equations of the multi-phase humid atmosphere expressed as a quasi variational inequality

et al. 2018

View full text Add to dashboard Cite

In this article we propose a new formulation of the equations of the humid atmosphere with a multi-phase saturation generalizing thus the model introduced in [TWu15] and [TWa15]. More precisely, we consider the more realistic situation where the humid atmosphere comprises these components, namely water vapor, liquid water and cloud condensates and furthermore the saturation concentration is not constant. With the additional constraint that the vapor mass ratio q v is less than the saturation concentration q vs , which depends itself on the state, we are led, from the mathematical point of view, to introduce and handle a system of equations and inequations involving some quasi-variational inequalities for which we prove the existence of solutions.

show abstract

Global well-posedness for passively transported nonlinear moisture dynamics with phase changes

Cited by 24 publications

References 40 publications

Analyticity of solutions to the primitive equations

Analyticity of solutions to the primitive equations

Zero Mach Number Limit of the Compressible Primitive Equations: Well-Prepared Initial Data

The equations of the multi-phase humid atmosphere expressed as a quasi variational inequality

Contact Info

Product

Resources

About